Young tracks of hotspots and current plate...

Geophys. J. Int. (2002) 150, 321–361

Young tracks of hotspots and current plate velocities

Alice E. Gripp1,∗ and Richard G. Gordon2

1Department of Geological Sciences, University of Oregon, Eugene, OR 97401, USA2Department of Earth Science MS-126, Rice University, Houston, TX 77005, USA. E-mail: [email protected]

Accepted 2001 October 5. Received 2001 October 5; in original form 2000 December 20

S U M M A R YPlate motions relative to the hotspots over the past 4 to 7 Myr are investigated with a goalof determining the shortest time interval over which reliable volcanic propagation rates andsegment trends can be estimated. The rate and trend uncertainties are objectively determinedfrom the dispersion of volcano age and of volcano location and are used to test the mutualconsistency of the trends and rates. Ten hotspot data sets are constructed from overlapping timeintervals with various durations and starting times. Our preferred hotspot data set, HS3, consistsof two volcanic propagation rates and eleven segment trends from four plates. It averages platemotion over the past ≈5.8 Myr, which is almost twice the length of time (3.2 Myr) over whichthe NUVEL-1A global set of relative plate angular velocities is estimated. HS3-NUVEL1A,our preferred set of angular velocities of 15 plates relative to the hotspots, was constructedfrom the HS3 data set while constraining the relative plate angular velocities to consistencywith NUVEL-1A. No hotspots are in significant relative motion, but the 95 per cent confidencelimit on motion is typically ±20 to ±40 km Myr−1 and ranges up to ±145 km Myr−1. Theuncertainties of the new angular velocities of plates relative to the hotspots are smaller thanthose of previously published HS2-NUVEL1 (Gripp & Gordon 1990), while being averagedover a shorter and much more uniform time interval. Nine of the fourteen HS2-NUVEL1angular velocities lie outside the 95 per cent confidence region of the corresponding HS3-NUVEL1A angular velocity, while all fourteen of the HS3-NUVEL1A angular velocities lieinside the 95 per cent confidence region of the corresponding HS2-NUVEL1 angular velocity.The HS2-NUVEL1 Pacific Plate angular velocity lies inside the 95 per cent confidence regionof the HS3-NUVEL1A Pacific Plate angular velocity, but the 0 to 3 Ma Pacific Plate angularvelocity of Wessel & Kroenke (1997) lies far outside the confidence region. We show that thechange in trend of the Hawaiian hotspot over the past 2 to 3 Myr has no counterpart on otherchains and therefore provides no basis for inferring a change in Pacific Plate motion relative toglobal hotspots. The current angular velocity of the Pacific Plate can be shown to differ fromthe average over the past 47 Myr in rate but not in orientation, with the current rotation beingabout 50 per cent faster (1.06 ± 0.10 deg Myr−1) than the average (0.70 deg Myr−1) since the47-Myr-old bend in the Hawaiian–Emperor chain.

Key words: Galapagos, Hawaii, hotspots, Pacific Plate, plate tectonics, volcanoes.

I N T R O D U C T I O N

A global set of current angular velocities of the plates relative tothe hotspots is a benchmark for motion between hotspots, the in-teraction between spreading ridges and hotspots, recent changes inplate velocity relative to the hotspots, plate-driving forces and aterrestrial reference frame tied to the deeper Earth through surfaceobservations. For prior global estimates of current plate angular ve-

∗Now at: Santa Barbara Orchid Estate, 1250 Orchid Drive, Santa Barbara,CA 93111, USA. E-mail: [email protected]

locities relative to the hotspots, uncertainties in the segment trendsand rates of volcanic propagation, though carefully considered, hadbeen subjectively estimated and the age span of incorporated volca-noes varied considerably (Minster et al. 1974; Chase 1978; Minster& Jordan 1978; Gripp & Gordon 1990). Here we present a methodfor objectively estimating the uncertainty of the segment trends andincorporate them into our estimates of plate angular velocity. Wetabulate ages of young hotspot volcanoes based as much as possi-ble on consistent horizons, estimate the time it takes the bulk of ahotspot volcano to grow and check the consistency between volcanoages and plate speed.

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322 A. E. Gripp and R. G. Gordon

Our investigation is aimed at answering the following questions:

(1) What is the best estimate of the current angular velocities ofthe plates relative to the hotspots?

(2) What is the best estimate of the uncertainties in the currentangular velocities of plates relative to the hotspots? How do theseuncertainties compare with prior estimates?

(3) How can one objectively estimate the uncertainties of thetrends of hotspot tracks? Are these uncertainties consistent withthose estimated before? In particular, are the uncertainties previ-ously assumed for trends on slow-moving plates realistic?

(4) Over how short a time interval can one use hotspot tracksand still obtain usefully accurate plate motions? What’s the besttime interval to use?

(5) Are previously published estimates of current plate velocitiesrelative to the hotspots consistent with the data now available?

(6) Does the current angular velocity of the Pacific Plate relativeto the hotspots differ significantly from that averaged over the past≈47 Myr, i.e. the time interval represented by the entire Hawaiianridge (Sharp & Clague 1999)?

(7) Are the patterns of plate rms velocities consistent with thosefound before?

(8) Do ages obtained from the tops of hotspot volcanoes accu-rately reflect the age at which most of the volcano formed?

The question of possible and appropriate time span is impor-tant for several reasons. NUVEL-1A, the global set of currentrelative plate angular velocities used herein, averages plate mo-tion over a time span no longer than ≈3.2 Myr, the time inter-val over which nearly all of its spreading rates were determined(DeMets et al. 1990, 1994). There is convincing evidence thatthe motion of the Pacific Plate, which carries most of the usefulhotspot tracks, changed direction by 8◦ and increased in rate byabout 20 per cent relative to the Antarctic Plate at ≈6 to ≈8 Ma.At the same time it also changed direction by 20◦ to 25◦ rela-tive to the North American Plate (Cande et al. 1995; Atwater &Stock 1998). In contrast, prior global hotspot data sets incorpo-rated observations from some tracks spanning 10 to 30 Myr orlonger. Thus, a new global hotspot data set spanning less than6 to 8 Myr is needed.

Toward that end, we have determined a new set of angular ve-locities of the plates relative to hotspots that are consistent with theNUVEL-1A angular velocities. The new set of angular velocities,which we refer to as HS3-NUVEL1A, are based on a data set, HS3,of hotspot segment trends and volcanic propagation rates that av-erage plate motion relative to the hotspots over the past ≈5.8 Myr.We chose this interval in part because it is the longest interval thatis most likely to exclude the most recent major change in Pacific–Antarctic relative plate motion, which may have occurred as recentlyas 5.9 Ma (Cande et al. 1995).

Herein we use units of millions of years (Myr) and kilometers(km) because they are appropriate to hotspot volcanoes. A predictedtrend or rate is one estimated from a set of angular velocities con-structed from data that exclude that trend or rate. In contrast, acalculated trend or rate is one estimated from a set of angular ve-locities constructed from data that include that trend or rate. Weconsider ‘hotspots’ to be surface features. When we use the phrase‘motion between hotspots’, it refers only to motion between loci ofvolcanism. No implications are intended about relative motion oftheir sublithospheric sources.

In evaluating statistical differences, herein we use the 95 per centconfidence level, which is equivalent to a 5 per cent level of signif-icance, as the confidence level is one (or 100 per cent) minus the

significance level. In some cases, a result may lie just outside orinside the 95 per cent confidence limit and in other cases well out-side or inside the limit. To convey additional information about howwidely or narrowly a null hypothesis passed or failed, we also quote,usually parenthetically, the value of p, which is the probability ofobtaining data as different or more different from the null hypothesisas the data we use. Barring bad luck, the smaller the value of p, theless likely that the null hypothesis is true.

M E T H O D S A N D R E S U L T S

We analyse hotspot data, uncertainties and model assumptions atfour levels. First, we assign an age and a location to the volcanoes atthe young end of each promising hotspot track—those with youngislands or well-studied seamounts (tracks used in HS3-NUVEL1Aare listed in Table 1 and Appendix A; see Gripp (1994) for a list ofother hotspots considered but discarded). Second, for segments withenough young volcanoes, we estimate segment trends and volcanicpropagation rates by least-squares. Third, we estimate a global set ofangular velocities of the plates relative to the hotspots, while fixingrelative plate angular velocities to those of NUVEL-1A (DeMetset al. 1990, 1994). Fourth, we compare results for hotspot data aver-aged over ten overlapping time intervals with various starting timesand durations.

Level one: volcano age and location

Our first-tier analysis consists of assigning volcano age and volcanolocation (Table 1), which are needed to estimate segment trend orvolcanic propagation rate. We require that the volcano formed off-ridge (for Galapagos we use only the near-ridge, not the on-ridge,part of the track to measure trend), that a submarine volcano has beensampled (not just known from bathymetry) and that the volcano isyoung. To qualify as young, all rocks sampled from an edifice mustbe young and if the effective elastic thickness has been estimatedfor the underlying lithosphere, the thickness must be consistent withthe edifice having a young age.

Volcano location

Unlike spreading centres, where young eruptions and intrusions oc-cur within 1 to 5 km of the spreading centre axis (Macdonald 1986),hotspot volcanism is less localized. For example, Loihi, Kilauea andMauna Loa, which are the three Hawaiian volcanoes in their mainphase of construction, are separated by 60 km along trend (Table 1,Appendix A). Within the past 30 000 yr, volcanism has occurred overa 375 km length of the Hawaiian Ridge. Thus the 0 Ma isochronfor Hawaii is an undulating, subhorizontal surface (Moore 1987),which cannot be drawn as a single line or point on a map. Even asingle volcano is hardly a point because one volcano may be 100 kmwide and have several rift zones and many vents.

To keep the analysis simple, however, we assign a single geo-graphic point to each volcano. For volcanoes with summit calderas,which include ≈30 per cent of all volcanoes, we take the location ofeach volcano to be the centre of its summit caldera or the intersectionof its rift zones. For ≈10 per cent of the volcanoes, usually thosethat are older and eroded, there is indirect evidence for the locationof a summit caldera. For the remaining volcanoes (≈60 per cent)we use the geographic centre or summit.

Volcano age

Although a typical hotspot volcano erupts subaerially for at leastseveral million years (Appendix A), the length of time it takes for a

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Young tracks of hotspots 323

Table 1. Data from individual volcanoes.

Volcano Location, Age ±1σ , Description and age basisN◦, E◦ Myr old

Easter-Sala y Gomez (Nazca) Age ≡ Oldest, Moderately Reliable Age from the ‘Main Group’Ahu Volcanic Field −26.58, −110.94a Active 2700-km2 tholeiitic submarine lava field made up of ridges and seamounts; degree

of sample alteration ranges from fresh glass to mm-thin Fe-Mn oxide crusts(Stoffers et al. 1994; Haase et al. 1996)

Umu Volcanic Field −26.96, −111.05b Active 1700-km2 tholeiitic submarine lava field made up of ridges; degree of samplealteration ranges from fresh to thin crusts (Stoffers et al. 1994;Fretzdorff et al. 1996)

Tupa Volcanic Field −27.90, −110.50c Active? Small, tholeiitic volcanic field (or seamount); samples are covered by Fe-Mn crustssimilar to those on Ahu and Umu (Stoffers et al. 1994; Haase & Devey 1996)

Pukao Seamount −26.95, −110.26d <0.63 ± 0.18 Ar-Ar plateau age (O’Connor et al. 1995) from the Volcanic Field Group, whichseems to predate the Main Group (Haase et al. 1997)

Moai Seamount −27.10, −109.68d 0.23 ± 0.08 Ar-Ar plateau age (O’Connor et al. 1995) from the Main Group (Haase et al. 1997)Tereveka volcano −27.09, −109.38e 0.25 ± 0.05 Fissure volcano (Baker et al. 1974); hawaiite from the oldest series of the main

shield dated by K-Ar (Clark 1975)Rano Kau volcano −27.19, −109.44e 0.98 ± 0.19 Strato-volcano (Baker et al. 1974); K-Ar date on feldspar separates from a basalt at

the base of a sea cliff (Clark 1975)Poike volcano −27.11, −109.26e 0.69 ± 0.13 Whole-rock, K-Ar date on an olivine basalt from the deepest outcrop of the volcano

(Kaneoka & Katsui 1985), which belongs to the Main Group (Haase et al. 1997);Clark (1975) reports an age of 2.61 ± 0.28 Ma for a similarly located sample

Sala y Gomez −26.46, −105.46 f 2.00 ± 0.07 Dredged hawaiite dated by K-Ar (Clark 1975) of unknown group; the tinyIsland island comprises two eroded mugearite flows (Fisher & Norris 1960)

one of which has a K-Ar date of 1.38 ± 0.04 Ma (Clark 1975)

Galapagos (Nazca) Age ≡ Oldest Moderately Reliable Age EstimateIsla Darwin 1.65, −92.00g 0.41 ± 0.16 Rock dated by K-Ar (White et al. 1993); island itself is a tiny eroded summit of

(Culpepper) this volcano (McBirney & Williams 1969)Isla Wolf (Wenman) 1.37, −91.82g 1.60 ± 0.07 Rock dated by K-Ar (White et al. 1993); island itself is a tiny eroded summit of

this volcano (McBirney & Williams 1969)Roca Redonda 0.27, −91.62h Active Active fumaroles occur on this small eroded remnant of an alkalic-lava-filled

crater (Standish et al. 1998)Ecuador Volcano −0.02, −91.56i 0.092 ± 0.035 Normally polarized sample dated by K-Ar (Cox & Dalrymple 1966) from this

(Cape Berkeley) eroded volcano (McBirney & Williams 1969); although extinct, its composition,unstable isotopic ratios, and trace elements are most similar to thoseof the active volcanoes of Roca Redonda and Cerro Azul (Standish et al. 1998)

Fernandina Island −0.36, −91.54 j Active Historic eruptions on the tholeiitic shield (Richards 1962;(Narborough) McBirney & Williams 1969)

Cerro Azul volcano −0.92, −91.42 j Active Historic eruptions on this shield volcano (Naumann & Geist 2000)Volcan Wolf 0.02, −91.36 j Active Historic eruptions on this shield volcano (Richards 1962)Volcan Darwin −0.19, −91.29 j Active Very fresh lava flows on this shield volcano (Richards 1962)Sierra Negra vol. −0.81, −91.12 j Active Historic eruptions on this shield volcano (Reynolds et al. 1995)Alcedo volcano −0.42, −91.12 j Active Historic eruptions on this shield volcano (Geist et al. 1994)Pinta Island 0.59, −90.75g ≈0.78 Normally magnetized transitional shield volcano modified by normally magnetized

(Abingdon) late fissure eruptions (Cullen & McBirney 1987); shield rock gives an age of0.89 ± 0.24 Ma (White et al. 1993)

San Salvador Isl. −0.22, −90.77k 0.78 Alkalic shield partially covered by younger flows; all lava flows are normally(James, Santiago) magnetized and the oldest K-Ar date is 0.79 ± 0.12 Ma (Swanson et al. 1974)

Rabida Island −0.41, −90.70k 0.99–1.07 Tholeiitic shield volcano; normally magnetized (Jaramillo?) shield is overlain by(Jervis) reversely magnetized rocks; average date from the scattered, stratigraphically

inconsistent K-Ar dates is 1.0 Ma (Swanson et al. 1974)Pinzon Island −0.61, −90.66k 1.40 ± 0.08 Rock dated by K-Ar (White et al. 1993) from this tholeiitic volcano

(Duncan) (Swanson et al. 1974)Marchena Island 0.35, −90.46g 0.56 ± 0.04 Basalt fragment in tephra from the transitional shield volcano (Vicenzi et al. 1990)

(Bindloe) dated by K-Ar (White et al. 1993)Santa Maria Island −1.29, −90.45k 1.52 ± 0.08 Alkalic basanatoid from the alkalic shield (Bow 1979) dated by K-Ar

(Charles, Floreana) (White et al. 1993)Santa Cruz Island −0.64, −90.36k 2.1 ± 0.5 K-Ar date of rock from the tholeiitic platform series (the oldest rocks on the

(Indefatigable) island), after which follow the eruption of a shield made of M0RB-like tholeiiticbasalts and alkalic basalts (Bow 1979; date from J. Dymond, pers. comm.)

Santa Fe Island −0.81, −90.08k 2.82 ± 0.05 Weighted average K-Ar date on a basalt (Bailey 1976) from the transitional volcano(Barrington) (Geist et al. 1985; White et al. 1993)

Genovesa Island 0.33, −89.96g 0.0 Rock with no detectable radiogenic Ar (White et al. 1993); island is tholeiitic(Tower) (White et al. 1993) and consists of a shield cut by younger fissure eruptions

(McBirney & Williams 1969)

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Table 1. (Continued.)


Espanola Island −1.38, −89.70k 3.40 ± 0.36 Eroded alkalic shield volcano (Hall 1983); basalt dated by K-Ar (Bailey 1976)(Hood)

San Christobal −0.91, −89.52k 2.35 ± 0.03 K-Ar date on an alkaline rock (White et al. 1993) from the normally polarized alkalicIsland (Chatham) flood basalts that underlie a shield and fissure eruptions composed of alkalic basalts,

OIB tholeiitic basalts, MORB-like tholeiitic basalts, and all of their differentiates(Geist et al. 1986) of reversed and normal polarity (Cox 1971); however this K-Ardate is inconsistent with magnetic time scale of Hilgen (1991a)

Unnamed seamount −1.19, −89.11l 5.8 ± 0.8 Ar-Ar plateau age from an aphyric highly vesicular moderately altered basalt(Sinton et al. 1996)

Hawaii (Pacific) Age ≡ Age of Shield-Postshield TransitionLoihi Seamount 18.96, −155.26m Active Transitional between preshield and shield stages (Moore et al. 1982; Garcia et al. 1995)Kilauea Volcano 19.42, −155.27n Active Shield stage (Stearns 1940)Mauna Loa Volcano 19.48, −155.58o Active Shield stage (Stearns 1946)Mauna Kea Volcano 19.82, −155.47p 0.237 ± 0.031 Basalt dated by K-Ar from the lowest exposures of the Hamakua Volcanics (older

substage of the postshield stage) (Wolfe et al. 1997)Hualalai Volcano 19.69, −155.87p 0.133 ± 0.005 Reef dated by 234U/238U (Ludwig et al. 1991) that is crossed by few tholeiitic flows

from Hualalai (Moore & Clague 1988)Kohala Volcano 20.08, −155.72p 0.261 ± 0.012 Mugearite with shield chemistry from uppermost Pololu Volcanics (shield stage) dated

by K-Ar (McDougall & Swanson 1972) reinterpreted by (Spengler & Garcia 1988)Mahukona Volcano 20.13, −156.24q 0.463 ± 0.004 Reef dated by 234U/238U (Ludwig et al. 1991) that probably formed at the end of

shield building as fewer flows were able to cross the shoreline(Clague & Moore 1991a,b; Moore & Clague 1992)

Haleakala Volcano 20.72, −156.22r 0.97 ± 0.04 Alkalic basalt dated by K-Ar from the uppermost part of the Honomanu Basalt (shield(East Maui) stage) (Chen et al. 1991)

Kahoolawe Volcano 20.54, −156.56r 0.99 ± 0.06 Tholeiitic basalt flow dated by K-Ar from the Kanapou Volcanics (shield and postshield),this date may be too young or the flow may a postshield flow (Fodor et al. 1992)

West Maui Volcano 20.88, −156.58r 1.33 Alkalic basalts near the top of the Wailuku Basalt (shield stage and caldera- fillinglavas of the postshield stage) (Langenheim & Clague 1987); average K-Ar agesfrom 3 flows (McDougall 1964)

Lanai Volcano 20.79, −156.91r 1.24 ± 0.06 Youngest K-Ar date from the Lanai Basalt (shield stage) (Bonhommet et al. 1977)East Molokai 21.14, −156.85r 1.53 Alkalic basalts from the upper part of the lower member of the East Molokai Volcanics;

Volcano average of 2 K-Ar dates (McDougall 1964)West Molokai 21.15, −157.12r 1.89 Tholeiitic flow near the top of the West Molokai Volcanics (shield and postshield)

Volcano dated by K-Ar (McDougall 1964); this age was reconfirmed by Clague (1987) whomeasured K-Ar dates of 1.73 to 1.80 Ma on overlying hawaiite flows

Penguin Bank 21.03, −157.58s Undated Probable submarine Hawaiian volcano (Macdonald & Abbott 1970; Clague 1996)Koolau Volcano 21.40, −157.76r 1.83 ± 0.25 Youngest K-Ar dates averaged from an outcrop of the Koolau Basalt (shield and

postshield) (Doell & Dalrymple 1973)Waianae Volcano 21.45, −158.15r 3.08 ± 0.02 Reversely polarized alkali basalt flow dated by K-Ar date from the Kamaileunu Member

(later shield stage), although this date is inconsistent with its having eruptedduring the Kaena reversed event (Guillou et al. 2000)

Kaena Ridge 21.67, −158.50s Undated Probable submarine Hawaiian volcano (Clague 1996)Haupu Volcano 21.93, −159.38t Young Once thought to be a flank caldera of Olokele (e.g. Langenheim & Clague 1987);

it is now thought to be a separate volcano (Clague 1996)Olokele Volcano 22.13, −159.51r 3.947 ± 0.046 Hawaiite dated by K-Ar from the top of the Waimea Canyon Basalt (shield and rare post

shield stages) (Clague & Dalrymple 1988)Niihau Volcano 21.94,−160.06u 4.89 ± 0.11 Tholeiitic flows and dikes from the Paniau Basalt (shield and postshield stages); date

from an unpublished K-Ar isochron by G. B. Dalrymple (1983, referenced byClague & Dalrymple 1987)

Kaula Island 21.66, −160.55v Young Small palagonitic tuff cone; accidental rock fragment of phonolite (likely fromposterosional stage) yields a K-Ar data of 4.01 ± 0.9 Ma (Garcia et al. 1986)

Juan Fernandez (Nazca) Age ≡ Oldest K-Ar DateFriday seamount −33.78, −81.71w Young Young alkalic basalts dredged from this seamount (Ken Farley, pers. comm, 1992)Alejandro Selkirk −33.76, −80.77x 2.44 ± 0.14 Basalt (Stuessy et al. 1984) from the moderately eroded volcano (Baker et al. 1987)

Isl. (Mas Afuera)Robinson Crusoe −33.63, −78.86x 4.23 ± 0.16 Basalt (Stuessy et al. 1984) from the deeply dissected volcanic island (Baker et al. 1987)

Isl. (Mas a Tierra)

Macdonald (Pacific) Age ≡ Oldest Moderately-Reliable Age EstimateMacdonald −28.98, −140.25y Active Volcanic eruption and magma movement detected from T-waves (Norris & Johnson 1969);

Seamount methane anomaly (Stoffers et al. 1989): a much older volcano was discovered on itsflank after this data set was finalized (J. Reynolds and K. Jordahl, pers. comm., 1999)

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Ra Seamount −28.77, −141.08y 29.21 ± 0.61 Whole rock Ar-Ar plateau age on a rock (McNutt et al. 1997) dredged from this1040-m deep guyot whose upper flank is covered with shallow-water indicators(Stoffers et al. 1989); features on summit are covered with thin Mn crusts (<2 mmthick) (Binard et al. 1992a)

Marotiri Rocks −27.91, −143.43z 31.95 ± 0.82 Whole rock Ar-Ar plateau age on a rock dredged from this mixed age volcano,whose young volcanism gives a whole rock Ar-Ar plateau age of 3.78 ± 0.18 Ma(McNutt et al. 1997)

Rapa Island −27.60, −144.34aa Poorly dated Dissected shield volcano (Chubb 1927); K-Ar dates range from 5.1 ± 0.2 to5.3 ± 1.7 Ma (Krummenacher & Noetzlin 1966), but many of the dates from thispaper have proved unreproducible

Marquesas (Pacific) Age = Oldest Moderately-Reliable K-Ar DateUnnamed seamount −10.82, −138.43bb 0.76 ± 0.10 Ar-Ar plateau age on a potassic trachyandesite (Desonie et al. 1993)Fatu Hiva Island −10.47, −138.66cc 2.46 ± 0.12 Lava flow (K2O = 0.77 wt. per cent) from the older of two concentric volcanoes, both

of which contain only hypersthene and nepheline normative basalts(Brousse et al. 1990)

Motu Nao Island −10.35, −138.44dd 1.27 ± 0.10 Ar-Ar plateau age on a potassic trachyandesite dredged from its SW flank(Desonie et al. 1993)

Motane Island −9.99, −138.80cc 2.26 ± 0.11 Lava flow (K2O = 1.17 wt. per cent) that belongs to a series that overlies an islandwide unconformity (Brousse et al. 1990)

Tahuata Island −9.96, −139.08cc 2.86 ± 0.14 Lava flow (K2O = 0.85 wt. per cent) from the lower half of the volcano(Brousse et al. 1990)

Unnamed seamount −9.90, −138.33ee Undated Unsampled seamountHiva Oa Island −9.77, −139.04 f f 2.74 ± 0.07 Basalt flow (K2O = 1.28 wt. per cent) with normal polarity (Katao et al. 1988)South H. F. −9.81, −139.60gg Undated Unsampled seamount in the Marquesas ridge

DumontD’urville Smt.

Fatu Huka Island −9.43, −138.92cc 2.65 ± 0.10 Alkalic basalt flow (K2O = 1.27 wt. per cent) (Brousse et al. 1990; name based onsilica and alkali content in Liotard & Barsczus 1983a)

North H. F. −9.58, −139.78gg 3.13 ± 0.14 Alkali olivine basalt dated by Ar-Ar total fusionDumont (Desonie et al. 1993)D’urville Smt.

Ua Pou Island −9.39, −140.06hh 5.61 ± 0.06 Tholeiitic rock (K2O = 0.78 wt. per cent) from the tholeiitic phase that spanned5.61–4.46 Ma; alkalic rocks erupted from 2.88–1.78 Ma (Duncan et al. 1986)

Ua Huka Island −8.93, −139.54cc 2.85 ± 0.02 Lava flow (K2O = 1.44 wt. per cent) (Duncan & McDougall 1974)Nuku Hiva Island −8.90, −140.09cc 4.31 ± 0.02 Weighted average dates of a beach cobble (K2O = 0.84 wt. per cent)

(Duncan & McDougall 1974)Hatu Iti Rocks −8.68, −140.62dd Young Three rocks, the westernmost is 200 m high (Chubb, 1930)

(Motu Iti Rocks)Banc Clark −8.07, −139.62gg Undated Unsampled bank in the Marquesas ridgeBanc J. Goguel −7.91, −139.96gg 5.30 ± 0.30 Oceanite (K2O = 0.48 wt. per cent) dredged from the 30-m-deep bank

(Brousse et al. 1990)Motu One Island −7.88, −140.39dd Young? 3-m-high island (Aeronautical Chart Service 1951) of uncertain composition

(Coral Island) (Chubb 1930); because coral is rare in the Marquesas (Chubb 1930), if really is atleast partly coral, it is likely that young basalt underlies it

Eiao Island −8.01, −140.68cc 5.56 ± 0.05 Quartz tholeiite from 754-m level of a 800-m-deep drill hole, which contains quartzand olivine tholeiites (800–686 m); hawaiites, mugearites, and trachytes(686–415 m); and olivine tholeiites and alkalic basalts (415–0 m), whichcontains at 122 m an alkali basalt with an age of 5.22 ± 0.06 Ma (Caroff et al. 1995)

Hatutu Island −7.91, −140.58cc 4.90 ± 0.20 Tholeiitic basalt (K2O = 0.81 wt. per cent) flow (Brousse et al., 1990; name basedon silica and alkali content in Liotard & Barsczus, 1983b)

Martin Vaz (South America) Age = Oldest Moderately-Reliable AgeIlha do Norte −20.47, −28.85i i Poorly dated Largest island in Ilhas Martin Vaz; the only K-Ar dates consist of 67.0 ± 1.4 Ma on an

ankaramite and <0.75 Ma on an hauynitite (Cordani 1970), the first of which isinconsistent with the island still being above sea level and the second of which may bemore likely, but given the difficulties with the first, it remains unreliable as well

Unnamed seamount −20.72, −29.20 j j Undated 2-km-deep, unsampled seamount on same ridge as the two main islandsTrindade Island −20.51, −29.33kk 3.35 ± 0.29 Nephelinite dyke dated by K-Ar (Cordani 1970) from the Trindade Complex, the basal

unit of the island (Almeida 1961)

Pitcairn (Pacific) Age = K-Ar Dates of the Approximate End of Shield BuildingAdams seamount −25.38, −129.26ll Young Fresh lava, but summit is covered with coral and coral sands and it may have a trachyte

dome on its summit (Stoffers et al. 1990; Binard et al. 1992b); the averageisotopic ratios from this volcano lie nearer the isotopic ratios of the posterosionalvolcanism on Pitcairn than do those of Bounty (Woodhead & Devey 1993)

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Bounty seamount −25.18, −129.41ll Active Fresh lava and methane anomalies (Stoffers et al. 1990; Binard et al. 1992b)Pitcairn Island −25.07, −130.10mm 0.86 ± 0.01 Weighted average of 2 dates on an hawaiite near the top of the Tedside Volcanics

(shield phase) (Duncan et al. 1974)Henderson Island −24.36, −128.33nn Undated Raised coral reef (Carter 1967)Oeno atoll −23.93, −130.75nn Undated Atoll (Carter 1967)Temoe atoll −23.35, −134.48oo Undated AtollIles Gambier −23.13, −134.93oo 5.66 ± 0.03 Lava flow from the top of Mt. Duff, which is a 430-m high remanent of this deeply

dissected volcano (Guillou et al. 1994)

Samoa (Pacific) Age ≡ Oldest, Relatively Reliable K-Ar DateRose Atoll −14.55, −168.15pp Undated Atoll east of the SamoaRockne Volcano −14.23, −169.05qq Active Fresh alkalic basalts dredged from this submarine volcano (Hart et al. 1999); it was,

however, dredged after this data set was finalized, at which time it was known onlyas an unsampled seamount discovered by Johnson (1984)

Lata shield −14.25, −169.46rr Young Main shield volcano on Tau Island (Stice & McCoy 1968)A’ofa and Sila −14.17, −169.64rr Young One or two shield volcanoes overlying pyroclastic cones on islands of Ofu and Olosega

shields (Stice & McCoy 1968)Pago Volcano −14.29, −170.67rr 1.54 ± 0.02 Dyke from shield part of the Pago Volcanics on Tutuila (McDougall 1985)PPT Seamount −14.86, −170.64ss Young Seamount with young alkalic rocks (Poreda & Farley 1992)Fagaloa Volcano −13.92, −171.53t t 2.65 ± 0.07 Transitional basalt from shield part of the Fagaloa Volcanics on Upolu

(Natland & Turner 1985)Savai’i Island −13.61, −172.48uu Young All sampled rocks are normally polarized (Keating 1985)Wallis Islands −13.27, −176.17uu 0.82 ± 0.03 Rock dredged offshore of this island (Duncan 1985); dates from one its islets

(Nukufetau) span 0.08 to 0.50 Ma (excluding a date of 172 Ma, which is consideredsuspect because the rock is as fresh as and has a composition similar to the othersamples) (Price et al. 1991); this young volcanism may overlie an older volcano(Duncan 1985), but this could still not account for the 172 Ma date becauseit is older than the underlying seafloor (Price et al. 1991)

Society (Pacific) Rate Age ≡ End of Shield BuildingVolcano 16 −18.28, −148.17y Active? Fresh lava flows on this 2750-m-deep seamount (Binard et al. 1991)Seismic Volcano 1 −17.40, −148.83vv Mixed One of several low volcanoes in a region called Seismic Volcanoes; this one has both

thickly Mn-coated low-K rocks and young alkalic rocks (Cheminee et al. 1989;Hekinian et al. 1991); 1985 earthquake swarms chronicled by Talandier & Okal(1987) coincided with this group of volcanoes (Cheminee et al. 1989)

Mehetia Island −17.88, −148.07y Active Tiny island <2 km-wide with a very young, 400 m-high cone (Binard et al. 1993);earthquake swarm on submarine flank (Talandier & Okal 1984)

Seamount Turoi −17.52, −148.95y Mixed 900-m-high made of thickly Mn-coated low-K rocks and minor amounts ofyoung alkalic volcanism (Hekinian et al. 1991; Binard et al. 1992a)

Volcano 17 −17.47, −147.97y Active Fresh alkalic rocks recovered from this seamount (Binard et al. 1991 N. Binard pers.comm., 1992)

Moua Pihaa −18.33, −148.53y Active Earthquake swarms on this seamount (Talandier & Kuster 1976);Seamount basalts similar to ones on Mehetia (Brousse 1984)

Rocard Seamount −17.65, −148.58y Active Earthquake swarms on this seamount (Talandier & Kuster 1976); popping trachytesand alkalic basalts (Cheminee et al. 1989; Hekinian et al. 1991)

Cyana Seamount −17.93, −148.75y Mixed 1800-m-high volcano with Fe- and Mn-coated pillows (Hekinian et al. 1991)and flanks smoothed by sediments, talus, and Mn crusts (Binard et al. 1992a);fresh trachytes recovered near its summit (Devey et al. 1990)

Teahitia Seamount −17.57, −148.82y Active Earthquake swarms on this seamount (Talandier & Kuster 1976); hydrothermalactivity (Hoffert et al. 1987); popping basanites (Hekinian et al. 1991)

Tahiti-Iti Volcano −17.80, −149.19ww 0.39 ± 0.01 Flow with youngest K-Ar date (Duncan & McDougall 1976)(Taiarapu)

Tahiti-Nui Volcano −17.63, −149.46ww 0.46 End of second shield-building episode dated by K-Ar (H. Guillou pers. comm., 1996)Moorea Island −17.52, −149.83ww 1.46 ± 0.02 End of subaerial volcanic activity dated by K-Ar (Guillou pers. comm, 1996)Tetiaroa Atoll −17.01, −149.56xx Undated Coral atoll of unknown originMaiao Island −17.67, −150.64xx 1.67 Youngest K-Ar date from the greatest concentration of dates (Diraison et al. 1991

referencing R. A. Duncan pers. comm. 1988)Huahine Island −16.76, −151.00xx 2.6 Age of the end of the Gauss normal chron (Hilgen 1991a) because no reversely

polarized rocks have been sampled and all but three samples (two of which are fromlate-stage trachytic intrusions) from (Duncan & McDougall 1976) andRoperch & Duncan (1990) yield ages greater than 2.6 Ma within their95 per cent confidence limits; we treat this as one volcano unlikeBrousse et al. (1983) and Diraison et al. (1991)

Raiatea Island −16.83, −151.45yy 2.52 ± 0.02 Alkali basalt flow dated by K/Ar from the uppermost part of this shield volcano(Blais et al. 1997)

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Tahaa Island −16.62, −151.51yy 2.8 Main shield building ended 2.8 Ma, although minor activity continued until 2.5 Ma(White et al. 1989)

Bora Bora Island −16.51, −151.75zz 3.21 ± 0.02 Dyke from shield that yields youngest K-Ar date (Duncan & McDougall 1976)Taupiti Atoll −16.25, −151.82xx 3.66 ± 0.013 Weighted average K-Ar date of a lava block thrown up on island during a hurricane

(Diraison et al. 1991)Maupiti Island −16.44, −152.26ab 4.05 ± 0.03 Biotite-bearing olivine dolerite dyke dated by K-Ar that cuts shield rocks

(Duncan & McDougall 1976)

Yellowstone (North America) Age of Major Ash-Flow SheetsLow-velocity zone 44.71, −110.33ac Active? Upper crustal body with a low P-wave speed (4 km s−1) and a negative Bouguer

anomaly; these properties are consistent with a 10–50% partial melt of rhyolitecomposition, although these characteristics are also consistent with steam andwater-filled cracks (Schilly et al. 1982; Lehman et al. 1982)

Third-cycle 44.50, −110.64ad 0.602 ± 0.002 Weighted average of single-crystal Ar-Ar dates on sanidine from member B of thecaldera Lava Creek Tuff (Gansecki et al. 1998)

Second-cycle 44.31, −111.42ad 1.293 ± 0.006 Weighted average of single-crystal Ar-Ar dates on sanidine from the Mesa Falls Tuffcaldera (Gansecki et al. 1998)

First-cycle caldera 44.37, −110.92ad 2.003 ± 0.007 Weighted average of single-crystal Ar-Ar dates on sanidine from the HuckleberryRidge Tuff (Gansecki et al. 1998); oldest bimodal lavas erupted about 2.2 Ma(Christiansen, 1982; referencing K-Ar dates from J. D. Obradovich, writtencommunication, 1982)

Kilgore caldera 44.01, −111.94ae 4.3 Eruption of the Tuff of Kilgore (Morgan et al. 1984)Blue Creek caldera 43.76, −112.67ae 6.0 ± 0.2 Whole rock K-Ar date on the Tuff of the Blue Creek (Morgan 1988 referencing

Marvin, written communication, 1986)Blacktail caldera 43.74, −112.17ae 6.5 Eruption of the Tuff of Blacktail (Morgan et al. 1984)

Radiometric ages have been corrected to the decay constants of Steiger & Jager (1977). Magnetostratigraphy ages from Hilgen (1991a,b).aHighest peak from that part of the Ahu Volcanic Field surveyed by Stoffers et al. (1994).bSummit from map in Fretzdorff et al. (1996).cPosition of volcano (Stoffers et al. 1994).d Centre of seamount summit from bathymetry in Hagen et al. (1990).eCentre of summit caldera; summit caldera geometry from Chubb (1933); island location and topography the map of Defense Mapping Agency AerospaceCenter (1978).f Position of island from the map of Defense Mapping Agency Aerospace Center (1978).gIsland summit from the map of Defense Mapping Agency Aerospace Center (1990a).h Island centre from the map of Defense Mapping Agency Aerospace Center (1990a).i Approximate centre of a remnant volcano from map and description in McBirney & Williams (1969).j Approximate caldera centre from the map of Defense Mapping Agency Aerospace Center (1990b).k Island summit from the map of Defense Mapping Agency Aerospace Center (1990b).l Dredge location (Sinton et al. 1996).mSummit of seamount from map in Malahoff (1987).nProjected intersection of the rift zones at the summit caldera from a map in Holcomb (1987).oProjected intersection of the rift zones at the summit caldera from a map in Lockwood et al. (1987).pVolcano summit from the map of Defense Mapping Agency Aerospace Center (1969).q Position of volcano from map in Moore & Clague (1992).r Projected intersection of rift zones at the summit caldera from maps in Langenheim & Clague (1987).sApproximate centre of the possible Hawaiian volcano (David Clague, pers. comm., 1989).t Centre of caldera from map in Langenheim & Clague (1987).uExtrapolated centre of now-eroded Niihau’s summit caldera from sketch in Stearns & Macdonald (1947).vSummit of island from the map of Defense Mapping Agency Aerospace Center (1969).wApproximate summit of seamount (Ken Farley, pers. comm., 1992).x Volcano summit from the map of Defense Mapping Agency Aerospace Center (1975).yBinard et al. (1991).zPosition is based on the midpoint of four rocks shown on map of Director of Military Survey (1976a).aaCentre of bay on map of Director of Military Survey (1976a); centre of bay is roughly the centre of a collapsed caldera (Chubb 1927).bbDredge location (Desonie et al. 1993).ccCaldera centre (caldera geometry from Brousse et al. (1990); island location from map of Aeronautical Chart Service (1951)).dd Island centre from map of Aeronautical Chart Service (1951).eeApproximate centre of seamount from bathymetric map by Mammerickx (1992a).f f Centre of Atuona Caldera (caldera geometry from Gonzales-Marabal (1984); island location from map of Aeronautical Chart Service (1951)).ggCentre of seamount/bank from map in Liotard et al. (1986).hh Island summit from map of Aeronautical Chart Service (1951).i i Centre of main island from the map of Defense Mapping Agency Aerospace Center (1989a).j j Centre of seamount summit from bathymetry from Cherkis et al. (1989).

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kkHighest peak on island from map in Almeida (1961).ll Binard et al. (1992b).mmCaldera centre (caldera geometry from Carter (1967); island location from of Director of Military Survey (1976b)).nnApproximate centre of atoll from the map of Director of Military Survey (1976b).ooApproximate centre of lagoon from the map of Defense Mapping Agency Aerospace Center (1989b).ppCentre of atoll from the map of Defense Mapping Agency Aerospace Center (1976).qq Seamount summit (Johnson 1984).rr Centre of Bouguer gravity anomaly from map in Machesky (1965).ssCentre of PPT summit (as defined by the 1000-m contour) from map in Hawkins & Natland (1975).t t Centre of Fagaloa caldera; caldera geometry from Natland & Turner (1985), island location from the map of Defense Mapping Agency Aerospace Center(1976).uu Island summit from the map of Defense Mapping Agency Aerospace Center (1976).vvBinard et al. (1992a).wwCentre of plutonic complex from map in Williams (1933).xx Centre of island or atoll from the map of Defense Mapping Agency Aerospace Center (1983).yy Island summit from the map of Defense Mapping Agency Aerospace Center (1983).zzCaldera centre from map in Stark & Howland (1941).abIsland summit from the map of Defense Mapping Agency Aerospace Center (1973).acApproximate centre of the zone of 4 km s−1 P-wavespeed (Schilly et al. 1982).ad Caldera centre from outline in Christiansen (1984).aeCentre of caldera from outline in Pierce & Morgan (1992).

volcano to grow from the seafloor to the sea surface is poorly con-strained by observations. Growth of the main shield occurs rapidlyfollowed by a transition to eruptions at much lower rates and usuallywith different compositions and styles (McDougall & Duncan 1980;Clague & Dalrymple 1987). The duration of the whole volcanic cy-cle at a single hotspot volcano may be inversely related to plate speed(Emerick & Duncan 1982). It also appears likely that the length oftime of main shield building may be inversely related to plate speed,at least between Hawaii (≈100 km Myr−1) and Galapagos (≈20 kmMyr−1).

To keep the analysis simple, we assign a single instant in time toeach volcano based on the age of its exposed rocks and, rarely, rocksobtained from drilling. If the transition from high to low eruptiverate has been dated for many young volcanoes in a track, as forthe Hawaiian, Society and Yellowstone tracks, then we assign theage of this transition to be the volcano age. For volcanoes still intheir main stage of growth, as for Loihi, Kilauea and Mehetia, weassign a non-numerical age of active rather than using a too-olddate or guessing when the stage of high eruptive volume will end.For estimating volcanic propagation rates, we of course use only thenumerical ages. The non-numerical ages are essential, however, fordetermining which volcanoes to include when estimating trends.

For most hotspot tracks, no stages or horizons have been cor-related because the eruptive histories of the individual volcanoesare so dissimilar, the exposures are so poor, mapping is so limited,or the age estimates are so few. For these chains we generally as-sign volcano age as the oldest reliable age date unless the volcanois still in its main phase of growth. Many volcanoes have no ageestimates. We assign a non-numerical age of young if an undatedvolcano lies on young seafloor, if it is an undated volcanic island, orif it is a seamount from which only fresh or recently hydrothermallyaltered rocks have been dredged. A volcano may be composed ofboth young and old rocks. If dated, we assign to it the age of the ear-lier volcanism, otherwise we assign a non-numerical age of mixed.We assign a non-numerical age of undated to a volcano having nouseful estimate of age.

In principle, numerical age estimates should be increased by thelength of time it takes each volcano to grow from inception to theeruption of its dated horizon. To do so would be unrealistic, es-pecially because of the variable length of time it takes to growa volcano. Nevertheless one can use the age progression along a

chain to estimate the minimum length of time needed to build a vol-canic shield. Various straight-line fits to volcano ages versus distancealong the Hawaii and Society chains indicate that it takes 0.8 Myrto build volcanoes in either of these chains (Table 2, Appendix B).Thus the HS3-NUVEL1A angular velocities, which span active to5.0 Ma, average plate motions relative to the hotspots over the past≈5.8 Myr.

Level two: trends and rates and their uncertainties

Trends

The observed segment trend is the direction of plate motion relativeto a hotspot as delineated by its surface track for a specific timeinterval. Strictly speaking, the segments should be small circlesabout the (unknown) pole of rotation. For those short segments weexamine, however, the data are fit nearly as well by a great circleas by a small circle. The additional parameter needed to specify thecurvature of a small circle is highly uncertain and adds no usefulinformation (cf. Gordon et al. 1984). Consequently, we take theobserved segment trend to be the tangent to the great circle that bestfits the individual volcanoes of the time interval (Table 3). We solvefor the best-fit great circle by minimizing the following expression

Nvolc∑j=1

(m j · b)2 (1)

where Nvolc is the number of volcanoes in the segment, m j is theunit position vector of the jth volcano and b is the unit vector of thebest-fit pole.

We use exact error propagation, instead of a linearized approxi-mation, to propagate the uncertainty in chain width into uncertaintyin trend, i.e.

σtrend = tan−1

(σwidth

lobs/2

)(2)

where lobs is the observed length of the segment and σwidth is theacross-trend standard deviation of volcanoes in a hotspot track, asis discussed further below. The trend uncertainty is independent ofthe number of volcanoes within the segment and trends from shortsegments have greater uncertainty than those with long segments.

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Table 2. HS3-NUVEL1A active to 5 Ma rate observations.

Hotspot (Plate): Criteria and Comments Observed Age χ2aν Volcanic l = 0

Volcanoes used time error propagation interceptinterval (Myr) rate ( ± 1σ Ma)b

(Ma) (km Myr−1)

Hawaii (Pacific)Volcanoes with reasonably dated shield-postshield transition, age errors from radiometric dates

Mauna Kea, Hualalai, Haleakala, Kahoolawe, 0.1 to 4.9 date 28.7 107 ± 1 −0.78 ± 0.01West Molokai (σage = ± 1 Myr), Waianae, Niihau error (at Loihi)

Volcanoes with reasonably dated shield-postshield transition, age error from dispersionMauna Kea, Hualalai, Haleakala, Kahoolawe, 0.1 to 4.9 ± 0.19 ≡1.00 108 ± 5 −0.73 ± 0.13

West Molokai, Waianae, Niihau (at Loihi)

Volcanoes with reasonably dated shield-postshield transition, plus Mauna Loa, Kilauea,and Loihi set to 0.0 Ma, age error from dispersionLoihi (≡0.0 Ma), Kilauea (≡0.0 Ma), Mauna Loa 0.0 to 4.9 ± 0.27 ≡1.00 118 ± 7 −0.45 ± 0.13

(≡0.0 Ma), Mauna Kea, Hualalai, Haleakala, (at Loihi)Kahoolawe, West Molokai, Waianae, Niihau

Society (Pacific)Volcanoes with estimates for the end of shield building, age error from dispersion

Tahiti-Iti, Tahiti Nui, Moorea, Huahine, Raiatea, 0.4 to 4.0 ± 0.27 ≡1.00 106 ± 9 −0.74 ± 0.26Tahaa, Bora Bora, Maupiti (at Volcano 16)

aχ2ν is reduced chi-square and equals (χ2

rate)/ν, where ν is the number of degrees of freedom, which in this case isthe number of volcanoes minus 2.bl is the length along the observed segment trend measured from the young end of the segment.

Trend uncertainty

To estimate trend uncertainty (eq. 2), one needs an estimate of thewidth of hotspot segments, which we take to be the standard devia-tion of volcano location about the best-fitting great circle and whichcan be directly estimated for nine of the eleven chains. Values rangefrom 3 to 55 km (Table 3). Using a two-sided F-test to test the null hy-pothesis that two segments have the same standard deviation, we findthat 27 of 36 pairs of standard deviation are indistinguishable at the95 per cent confidence level (Table 4). Each of the nine that differ sig-nificantly include either Galapagos (whole archipelago; four of thecomparisons) or Yellowstone (six of the comparisons) or both (onecomparison). The significantly smaller Yellowstone standard devi-ation (7+19

−3 km, 95 per cent confidence level here and below), doesnot incorporate the ≈100 km width of the calderas (Appendix A)and we consider it no further. The significantly larger Galapagosstandard deviation (55+25

−13 km) reflects the existence of two sub-tracks, the Carnegie Ridge and the Wolf–Darwin lineament (Ap-pendix A). That Easter has the next largest sample standard deviation(43+52

−15 km) and that it differs more from Hawaii than from Galapa-gos, suggests that hotspots on young lithosphere have greater widthsthan those on older lithosphere.

All chains except Easter and Galapagos were assigned a 1σ widthof 33 km, which is the average of the 1σ width for Hawaii andSociety, the two chains with the best data. This agrees well withthe weighted average 1σ width of the Hawaiian, Juan Fernandez,Marquesas, Pitcairn, Samoa and Society chains, which is 32+8

−6 km(95 per cent confidence limits). We assign a larger 1σ width of55 km to the two hotspots (Easter and Galapagos) that are on younglithosphere.

Rates

Volcanic propagation rate was estimated from the slope of the linethat best fits assigned volcano age vs length along the chain, withage taken as the dependent variable and distance as the independentvariable. We omit age dates from active volcanoes, because the use

of dates within the active phase would bias the volcanic propagationrates upward. For example, if we had set the ages of Mauna Loa,Kilauea and Loihi, which are all active, to 0.0 Ma, then the estimatedHawaiian rate would have been 10 km Myr−1 greater than the ratewe use (Table 2). Rates are estimated only for chains where a some-what consistent horizon has been dated for many volcanoes, whichleaves only the Hawaiian and Society tracks, both on the PacificPlate.

Rate uncertainty

We consider two estimates of age uncertainty: analytical uncertaintyand standard deviation. In practice, the rate regression with ana-lytical uncertainties has values of χ2

rate that are unacceptably large(Table 2, column 4). For example, the fit to Hawaiian volcano agesgives a value of 29 for χ 2

ν (reduced chi-square, i.e. χ2 divided by ν,the number of degrees of freedom, where ν equals the number ofdata minus the number of adjustable parameters). The probability,p, of finding a value of χ2

ν this large or larger if these uncertaintieswere appropriate is only 10−29. Thus, dispersion of ages about astraight-line fit vs distance indicates a much larger uncertainty thanthat expected for a high-quality radiometric date. Thus, the esti-mated standard deviation leads to more realistic uncertainties in thepropagation rates than do the analytical uncertainties.

Level three: estimating angular velocities

The angular velocities of plates relative to the hotspots are deter-mined from a grid search for the minimum weighted, least-squareserror,

χ2hotspot ≡

N∑i=1

(dobs

i − dcali

σi

)2

(3)

where dobsi is the ith datum (rate or trend), dcal

i is the value calculatedfrom the grid value for the ith datum, σi is the standard error of the ithdatum and N is the number of data. A global set of angular velocities

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Table 3. HS3-NUVEL1A active to 5 Ma trend observations.

Hotspot (Plate) Observed Number of Observed |σwidth| Observed σtrend

volcanoes used time interval volcanoes azimuth ±95% length(Ma) of trend (km)a (km)

Easter (Nazca)Tupa, Umu, Ahu, Pukoa, Moai, Tereveka, Active to 1.0 8 098.6◦ 43+52

−15 178 ± 31.7◦ b

Rano Kau, Poike

Galapagos (Nazca)Subaerial volcanoes from the whole archipelago

Isla Darwin, Isla Wolf, Pinta, Marchena, Active to 3.4 21 140.3◦ 55+25−13 423 ± 14.6◦ b

Genovesa, Roca Redonda, Fernandina, Ecuador,Cerro Azul, Volcan Wolf, Volcan Darwin,Sierra Negra, Alcedo, San Salvador, Rabida,Pinzon, Santa Maria, Santa Cruz, Santa Fe,Espanola, San Christobal

Only subaerial volcanoes that lie on the Carnegie RidgeRoca Redonda, Fernandina, Ecuador, Cerro Azul, Active to 3.4 16 121.3◦ 33+19

−9 278 ± 21.6◦ b

Volcan Wolf, Volcan Darwin, Sierra Negra,Alcedo, San Salvador, Rabida, Pinzon, SantaMaria, Santa Cruz, Santa Fe, Espanola,San Christobal

Subaerial volcanoes from the Wolf–Darwin lineamentIsla Darwin, Isla Wolf, Pinta, Marchena, Genovesa 0.0 to 1.6 5 124.5◦ 15+40

−6 270 ± 22.2◦ b

Hawaii (Pacific)Loihi, Kilauea, Mauna Loa, Mauna Kea, Active to 4.9 18 303.5◦ 33+17

−9 600 ± 6.3◦Hualalai, Kohala, Mahukona, Haleakala,Kahoolawe, West Maui, Lanai, EastMolokai, West Molokai, Koolau, Waianae,Haupu, Olokele, Niihau

Juan Fernandez (Nazca)Friday, Alejandro Selkirk, Robinson Crusoe Young to 4.2 3 086.4◦ 3+30

−2 264 ± 14.0◦

Macdonald (Pacific)Macdonald, Rapa Active to ≈5c 2 291.0◦ NMd 429 ± 8.7◦

Marquesas (Pacific)Fatu Hiva, Motu Nao, Motane, Tahuata, ≈3 to ≈5c 11 310.0◦ 28+23

−9 302 ± 12.3◦Hiva Oa, Fatu Huka, N. Dumont, Ua Pou,Ua Huka, Nuku Hiva, Hatu Iti

Martin Vaz (South America)Ilha do Norte, Trindade Young to 3.4 2 264.9◦ NMd 50 ± 52.7◦

Pitcairn (Pacific)Adams, Bounty, Pitcairn Active to 0.9 3 289.1◦ 12+104

−6 91 ± 35.9◦

Samoa (Pacific)Lata, A’ofa-Sila, Pago, PPT, Fagaloa, Savai’i ≈0.5 to ≈3 c 6 283.2◦ 42+78

−17 334 ± 11.2◦

Society (Pacific)16, Mehetia, 17, Moua Pihaa, Rocard, Teahitia, Active to 4.0 16 292.6◦ 32+19

−9 479 ± 7.8◦Tahiti-Iti, Tahiti Nui, Moorea, Maiao, Huahine,Raiatea, Tahaa, Bora Bora, Taupiti, Maupiti

Yellowstone (North America)low velocity zone, third-cycle caldera, Active to 4.3 5 241.0◦ 7+19

−3 150 ± 23.8◦second-cycle caldera, first-cycle caldera, Kilgore

aσwidth ≡ s, which is the sample standard deviation of width estimated for each hotspot. The 95 per cent confidence limit of

σwidth is s[(n − 2)/χ20.975]

12 ≤ σwidth ≤ s[(n − 2)/χ2

0.025]12 , where χ2

0.975 and χ20.025 are evaluated for n − 2 degrees of freedom

and n is the number of volcanoes (Spiegel 1975).b Young seafloor σwidth = ± 55 km. Old seafloor or continent σwidth = ± 33 km.c ≈ denotes guessed age based on better volcano ages along the track.d NM ≡ ‘not meaningful’. These statistics could not be meaningfully calculated because there are only two volcanoes.

uses all rates and trends from a given time interval. While testingour assumptions, we also invert a variety of data subsets to study theorigin and measure the significance of the misfit to the hotspot data.A trend-only set of angular velocities uses all trends from a given

time interval. We assess the influence of a single hotspot datum(either trend or rate) by removing that datum and then re-invertingthe resulting smaller data set and using the results to predict thatdatum. From this analysis we can estimate one component of motion

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Table 4. F-values and significance (two-sided) of differences between width sample standard deviations.

Hotspot → Galapagos Easter Samoa Hawaii Galapagos Society Marquesas Pitcairn Yellow- Juanwidth → Track ±43 km ±42 km ±33 km Carnegie ±32 km ±28 km ±12 km stone FernandezHotspot ±55 km v = 6 v = 4 v = 16 ±33 km v = 14 v = 9 v = 1 ±7 km ±3 km

v = 19 v = 14 v = 3 v = 1

Galapagos 1.0 — — — — — — — — —Track

Easter 1.6 1.0 — — — — — — — —(58%)

Samoa 1.8 1.1 1.0 — — — — — — —(62%) (98%)

Hawaii 2.7 1.7 1.5 1.0 — — — — — —(5%) (38%) (48%)

Galapagos 2.8 1.7 1.6 1.0 1.0 — — — — —Carnegie (6%) (38%) (47%) (97%)Society 2.9 1.8 1.7 1.1 1.1 1.0 — — — —

(5%) (34%) (43%) (90%) (93%)Marquesas 4.0 2.5 2.3 1.5 1.4 1.4 1.0 — — —

(4%) (21%) (28%) (56%) (58%) (64%)Pitcairn 22.5 14.0 12.8 8.3 8.1 7.8 5.6 1.0 — —

(33%) (40%) (41%) (53%) (54%) (55%) (63%)Yellowstone 63.5 39.6 36.2 23.6 23.0 21.9 15.9 2.8 1.0 —

(1%) (1%) (1%) (2%) (3%) (3%) (4%) (38%)Juan 227.8 173.0 158.1 103.1 100.6 95.8 69.4 12.4 4.4 1.0Fernandez (9%) (12%) (12%) (15%) (16%) (16%) (19%) (35%) (67%)

— F-values and probabilities are not listed because the probability is equal to that of the opposite pair across the diagonal.F-values in bold have probabilities of ≤5%.

(trend-perpendicular for a trend, trend-parallel for a rate) of any onehotspot relative to other hotspots from the difference between theobserved and predicted datum.

Data importance, Ii , provides an estimate of the information con-tribution of the ith datum to its calculated value (Minster et al. 1974).The sum of the data importances equals the number of independentadjustable parameters, which is 3.0 in this case. An importance of1.0 implies that there exists a reparametrization for which that da-tum completely specifies the value of one parameter. An importancenear zero indicates that a datum contributes little information to theestimated parameters.

Uncertainties in angular velocity relative to the hotspots are es-timated by linear propagation of errors. We found that statisticalparameters derived from linear propagation of errors agree wellwith the parameters from exact propagation, which indicates thatlinear propagation of errors is a useful approximation for our anal-ysis. We neglect the errors from the NUVEL-1A set of relativeplate angular velocities, for which 1-D standard errors are aboutone tenth the length of those of the hotspot errors. Because therelative plate motion errors are neglected, the 3 × 3 hotspot covari-ance matrix is invariant with respect to which plate is held fixed.We are aware that revised estimates of current global relative platevelocities are under construction. Because of tests we performedwith earlier estimates of relative plate motion, however, we be-lieve our conclusions about short-term motion between hotspotsand appropriate averaging interval are robust, although the angu-lar velocities of the plates relative to the hotspots will need somemodification when a new set of relative plate angular velocities isincorporated.

Trend fitting function

When determining angular velocities relative to the hotspots, wereplace (dobs

i −dcali ) in eq. (3) with sin(αi/2) where αi is the angular

difference between the observed and calculated trend (DeMets et al.1990).

Rate fitting function

In eq. (3), dobsi is the observed volcanic propagation rate and dcal

i

is the calculated volcanic propagation rate. It is unclear what isthe most appropriate fitting function to use for calculated volcanicpropagation rate. For some models for how a mantle plume interactswith the lithosphere, the appropriate function would be the projec-tion of the calculated velocity onto the observed trend (|vcal

i | cos αi )(Chase 1972). For other models, the appropriate function would bethe deprojection of the calculated velocity from the observed trend(|vcal

i |/ cos αi ), similar to apparent velocity. There is really no goodevidence to choose between these two fitting functions. Thus, wechoose to split the difference between them by using a third fittingfunction, the trend-independent formulation of Minster et al. (1974),which assumes dcal

i = |vcali |. These three fitting functions give identi-

cal results only if the trend calculated for a hotspot with an observedrate is identical to the observed trend. The difference in results fromthe fitting functions increases as the angle between a calculated andan observed trend increases.

For the time interval of active to 5 Ma the difference betweenobserved and calculated trends is 3.3◦ for Hawaii and 1.9◦ forSociety. Use of the Minster et al. (1974) fitting function results ina Pacific-hotspot rotation rate only 0.002 deg Myr−1 less than thatwhich would have resulted if the fitting function of Chase (1972)had been used instead.

Level four: evaluation and comparison of globalsets of angular velocities

Trends and rates were analysed from ten overlapping time spans:active to 3.2 Ma, active to 4.0 Ma, active to 5.0 Ma, active to

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Table 5. Inferred durations and their statistical implications.

Chain Inferred �tb Length σtrend Fd p(F)e

durationa (Myr)(Myr) Observed Predictedc Observed Predicted

(km) (km)

Easter 5.7 −0.1 178 181 ±31.7◦ g ±31.2◦ g — —Galapagos 12.7 +6.9 278 127 ±21.6◦ g ±40.9◦ g F9,14 = 3.6 2%Hawaii f 6.5 +0.7 600 534 ±6.3◦ ±7.0◦ F8,16 = 1.2 34%Juan Fernandez 8.2 +2.4 264 186 ±14.0◦ ±19.6◦ F9,1 = 2.0 51%Macdonald 3.6 −2.2 429 688 ±8.7◦ ±5.5◦ — —Marquesas 2.6 −3.2 302 686 ±12.3◦ ±5.5◦ — —Martin Vaz 1.0 −4.8 50 282 ±52.7◦ ±13.2◦ — —Pitcairn 0.8 −5.0 91 694 ±35.9◦ ±5.4◦ — —Samoa 2.8 −3.0 334 692 ±11.2◦ ±5.5◦ — —Society f 3.8 −2.0 479 733 ±7.8◦ ±5.1◦ — —Yellowstone 5.5 −0.3 150 158 ±23.8◦ ±22.7◦ — —

aInferred duration, tpred = lobs/|vpred|.b�t = tpred − tmodel = tpred − 5.8Myr.cPredicted length is the maximum predicted length and = tmodel/|vpred| = 5.8Myr/|vpred|.d F = (

σpredtrend

σ obstrend

)2.eProbabilities are for the one-tailed F-test. Probabilities = 5% are printed in bold.f Both rate and trend removed.gYoung seafloor σwidth = ±55 km.

6.0 Ma, 0.0 to 4.0 Ma, 0.0 to 5.0 Ma, 0.0 to 6.0 Ma, 1.0 to 5.0 Ma,1.0 to 6.0 Ma and 2.0 to 6.0 Ma. Results for the HS3-NUVEL1Aset of angular velocities are discussed separately below.

Influence on trend uncertainty of the consistencybetween volcano age and plate speed

The uncertainties assigned to trends depend on the observed segmentlength (Table 3), which in turn depends on observed volcano ageand location. If the observed segment lengths are greater than thetrue length formed during a time interval, then the results would benegatively affected in two ways. First, the trend would be assignedan uncertainty that was too small and thus would be given too muchweight in the analysis. Second, the trend would be biased towarddirections of motion outside the time interval. Most volcano agesare of insufficient accuracy and density to be used to predict segmentlength accurately. As an alternative the inferred duration (Table 5)is estimated using the observed segment length and plate speedspredicted from an interim data set which has trend uncertaintiesbased solely on segment length (Table 3).

Let tpredi ≡ lobs

i /|vpredi | be the duration inferred from the observed

segment length of the ith hotspot, where |vpredi | is the speed pre-

dicted from an estimated set of plate angular velocities relative tothe hotspots determined from all hotspot data except that of the ithhotspot. �ti , the difference between tpred

i and the assumed dura-tion of the model, ranges from −5.03 to +6.90 Myr for the timeinterval of active to 5.0 Ma (Table 5). A negative �t may be dueto a discontinuous hotspot track or to the track having been onlysparsely surveyed (e.g. Martin Vaz, Pitcairn and Samoa), but a pos-itive �t suggests along-trend motion of the hotspot, poor age dates,long-lasting volcanism, inaccuracies in the assumed relative platemotions or some combination of these. Galapagos, Juan Fernandezand Hawaii have positive �t’s.

The maximum predicted segment length can be estimated bymultiplying predicted speed by the duration (5.8 Myr). Applyingeq. (2) to this predicted length gives a minimum uncertainty for

the trend. We find that the only minimum trend uncertainties thatare significantly larger than those originally estimated are for theGalapagos segments that include active volcanism (e.g. Table 5).Most of the large positive �t’s for these Galapagos segments arelikely to be caused by the main stage of Galapagos growth lastinglonger than the 0.8 Myr duration estimated for Hawaii. Along theobserved Galapagos trend, active volcanoes span 110 km comparedwith 60 km for Hawaii (Appendix A). Measured along the predictedtrend (084.8◦), the active length is 85 km. When divided by the pre-dicted rate, this indicates a 3.9 Myr duration for the main stage ofGalapagos growth. To avoid overweighting the Galapagos data, weincreased the assigned trend uncertainty for the four data sets thatinclude active volcanism, including the active to 5 Ma data set, to bethe minimum trend uncertainty. As expected, the volume of the errorellipsoids increased and the Galapagos data importance decreased,but changes in angular velocities were minor.

Mutual consistency of trends and rates

When we invert the trend-only data subset of HS3, the trends (and as-signed uncertainties) are found to be mutually consistent (χ2 = 5.1with 8 degrees of freedom, p = 0.75) attesting to the mutual con-sistency of our objectively estimated errors and the assumption thatthe hotspots are fixed. When we invert the HS3 global data set (oftrends and rates), they are found to be mutually consistent (χ 2 = 8.0with 10 degrees of freedom, p = 0.63). Moreover, a one-sidedF-test of the significance of the decrease in chi-square when the ratesare removed from the global data set indicates that the decrease inmisfit (from 8.0 to 5.1) is insignificant for the active to 5 Ma intervalused for HS3-NUVEL1A. It is also insignificant for the nine othertime intervals. Thus, within the dispersion of the data and our errorbudget, the rates and trends are mutually consistent. This does notrequire that the difference between the global and trend-only angu-lar velocities is small for a given time interval. Indeed, the lengthof the vector difference in angular velocity ranges from 0.05 degMyr−1 (active to 5 Ma) to 0.91 deg Myr−1 (1 to 6 Ma).

C© 2002 RAS, GJI, 150, 321–361


Figure 1. Bathymetric map of the Hawaiian islands. Island outlines are thick lines and 2000 m contours are thin lines (Mammerickx 1989). Mercator projection(a) Solid triangles, Hawaiian volcanoes younger than 3.2 Ma; solid squares, Hawaiian volcanoes with ages between 2 to 6 Ma. Arrows are scaled to show thedisplacements over 4.0 Myr. Medium arrows show the observed Hawaiian motion for the time intervals of active to 3.2 Ma and 2.0 to 6.0 Ma. Thick arrowsshow motion calculated from the global models for the time intervals of active to 3.2 Ma and of 2.0 to 6.0 Ma and their 2-D 95 per cent confidence ellipses. Thinarrows show the motion predicted when the Hawaiian rate or Hawaiian trend is removed and the motion calculated when a non-Hawaiian datum is removed. (b)Same as (a), but with the arrows scaled to show the displacement over 5.8 Myr (corresponding to the duration of the HS3-NUVEL1A time interval of active to5.0 Ma). Solid squares, Hawaiian volcanoes younger than 5.0 Ma.

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Table 6. Excluded trend observations.

Hotspot (plate): comments Observed Predicted Observed ObservedVolcanoes used time interval duration length trend

(Ma) (Myr) (km) ( ±1σ )

Bowie (Pacific): Edifices contain mixture of young and old volcanism, current location uncertainBowie, Hodgkins, Dickins ≈0 to 4.1 3.2 161 332.0 ± 22.3◦

Cobb (Juan de Fuca): On-ridgeAxial, Son of Brown Bear, Thompson Active to 3.2 5.2 108 084.1 ± 45.6◦a

Cobb (Pacific): On-ridgeAxial, Brown Bear, Pipe, Cobb, Corn, Gluttony, Active to 5.2 4.1 224 326.9 ± 26.1◦a

Anger, Lust, Sloth

Comores (Africa (Somali)): Active volcano lies between two older volcanoes; Observed lengthfar greater than that predicted by a model that includes the Comores trendKarthala, La Grille, Moheli Active to 5.0 7.4 98 155.4 ± 34.0◦

Eastern Caroline (Pacific): Excessively scattered K-Ar datesKosrae, Pohnpei 1.4 to 5.2 4.7 553 288.5 ± 6.8◦

Islas Revillagigedo (Pacific): Likely not a hotspot, two volcanoes lie a top the Mathematician Ridge,which is an extinct spreading centreSan Benidicto, Socorro, Roca Partida, Clarion 0.3 to 2.4 5.1 426 259.2 ± 14.5◦a

Lord Howe (Australia): One volcano is too old, one is likely too old, the presumed youngest is unsampledFlinders, Balls Pyramid, Lord Howe ? to 6.9 4.5 353 350.9 ± 10.6◦

Louisville (Pacific): Only one sampled volcano with age ≤5.0 Ma138.1W, 139.2W ? to = 1.1 0.9 95 305.9 ± 34.8◦

Louisville (Pacific): On-ridge?, possibly not a hotspot trackHollister Ridge Active ? to ? 2.3 b 230b 306 ± 26◦a

Reunion (Africa (Somali)): The two youngest volcanoes are separated by only 30 km and lieon the same island. The third, older volcano is too old. The observed length is far greater than that predictedby a model that includes the Reunion trendFournaise, de Neige, Mauritius Active to 7.6 17.6 233 064.9 ± 15.8◦

Tasmantid (Australia): An earthquake does not a hotspot volcano make, known seamount too oldmb = 6.0 1983 earthquake, Gascoyne Active? to 6.4 5.3 420 008.4 ± 8.9◦

aYoung seafloor width standard error is ±55. Old seafloor width standard error is ±33 km.bLength is that part of the Hollister Ridge lying on seafloor formed since 5.8 Ma (based on the NUVEL-1A Antarctic–Pacific halfspreading rate of 39.0 km Myr−1). Trend measured by eye from a map constructed from the gravity grid of Sandwell & Smith (1995).

Solution stability and robustness

To evaluate solution stability for a given time interval, we examinethe difference in the predicted and calculated trends from all setsof angular velocities determined by removing one datum and re-inverting the remaining data. We found that removal of one datumcan cause large changes in predicted and calculated trends if aninterval is only 4 Myr long (Fig. 1a). For example, for the 2 to 6 Mainterval, removal of one datum causes the predicted and calculatedtrends of Hawaii to vary by as much as 34◦ (Fig. 1a). In contrast,for all data sets spanning 6 Myr, removal of one datum causes thepredicted and calculated trends of Hawaii to vary by no more than10◦ (e.g. Fig. 1b). These results suggest, but by no means prove, thata 6-Myr-long averaging interval gives a more stable solution thandoes a 4-Myr-long interval. In any event, they verify the stability ofthe results obtained for the HS3 data set for which the variation inpredicted and calculated Hawaiian trend is 6◦ (Fig. 1b).

Potential effect of including data that were rejected

Trends and rates. The trends of many hotspot tracks, including someused by prior workers, were rejected here for several reasons:

(1) the track formed on a spreading ridge,(2) the plate speed was too slow to make a meaningful trend,(3) the available dates are of poor quality, or

(4) there are fewer than two sampled volcanoes with ages of 5 Maor younger.

To assess the effect of the rejection of these hotspot tracks on theangular velocities of HS3-NUVEL1A, we estimate observed trendsfor eleven rejected tracks (Table 6), adding them singly to the HS3data set and then re-inverting the data (Table 7). We also did the samefor three rates excluded from the HS3 data set (Tables 8 and 9). Allrejected data, except the Comores trend, Reunion trend, Tasmantidtrend and Galapagos rate, have misfits (observed minus predicted)smaller than their combined 95 per cent confidence limits (Tables 7and 9). These same four data cause the largest changes in angularvelocity, but no change is significant at the 95 per cent confidencelevel. The addition of any single datum, except the Comores andReunion trends, decrease the volume of the resulting confidenceellipsoid by less than 15 per cent.

The Reunion trend has a data importance of one and decreases theerror volume by more than 90 per cent without increasing χ 2

hotspot

significantly. This result sounds promising, but must be rejected.The resulting African-hotspot pole of rotation is shifted just northof the Reunion hotspot; consequently, rotation about the pole couldnot have created the observed length of the corresponding track in40 Myr, much less in 5.8 Myr! The Reunion trend and rate, the latterof which was inferred from only two volcano ages, are incompatiblewith each other when included in the HS3 data set. The Comorestrack has the same problems, but no meaningful statistics could be

C© 2002 RAS, GJI, 150, 321–361


Table 7. Influence of some unacceptable trends.

Hotspot HS3-NUVEL1A predictions Observed Trend �vat Model including unacceptable trend

trend misfit (α) ±95%Rate ±1σ Trend ±1σ ±95% (km Myr−1) Calculated Ib V0−V

V0

c�χ2d

(km Myr−1) ±1σ trend ±1σ

Bowie 50.7 ± 4.5 323.8 ± 9.3◦ 332.0 ± 22.3◦ 8.2 ± 47.4◦ 7 ± 42 325.1 ± 8.6◦ 0.15 9% 0.1Cobb (JdF) 20.5 ± 7.5 036.0 ± 14.9◦ 084.1 ± 45.6◦e 48.1 ± 94.0◦ 15 ± 24 039.7 ± 13.1◦ 0.08 7% 1.0Cobb (PA) 54.7 ± 4.9 312.9 ± 8.2◦ 326.9 ± 26.1◦e 14.0 ± 53.6◦ 13 ± 50 314.3 ± 7.9◦ 0.09 6% 0.3Comores 13.3 ± 7.1 297.3 ± 19.5◦ 155.4 ± 34.0◦ −141.9 ± 76.8◦ −8 ± 15 161.2◦ ± NM f NM f NM f 3.8EasternCaroline 117.7 ± 5.7 296.8 ± 4.0◦ 288.5 ± 6.8◦ −8.3 ± 15.5◦ −17 ± 32 294.3 ± 3.6◦ 0.27 9% 1.0

IslasRevillagigedo 84.1 ± 6.1 284.9 ± 3.9◦ 259.2 ± 14.5◦ e −25.7 ± 29.4◦ −36 ± 39 283.2 ± 3.7◦ 0.06 5% 2.9Lord Howe 77.7 ± 8.0 345.9 ± 5.1◦ 350.9 ± 10.6◦ 5.0 ± 23.0◦ 7 ± 31 346.8 ± 4.6◦ 0.18 10% 0.2Louisville

(off-ridge) 103.4 ± 7.0 294.3 ± 3.2◦ 305.9 ± 34.8◦ 11.6 ± 68.5◦ 21 ± 121 294.4 ± 3.2◦ 0.01 0% 0.1Louisville

(on-ridge) 99.8 ± 7.1 295.4 ± 3.3◦ 306 ± 26◦e 11 ± 51◦ 18 ± 87 295.5 ± 3.3◦ 0.02 1% 0.2Reunion 13.3 ± 7.2 314.2 ± 19.2◦ 064.9 ± 15.8◦ 110.7 ± 48.8◦ 12 ± 13 063.1 ± 15.7◦ 1.00 95% 3.6Tasmantid 79.6 ± 8.0 346.2 ± 5.0◦ 008.4 ± 8.9◦ 22.2 ± 20.0◦ 30 ± 26 351.2 ± 4.2 0.22 14% 4.7Non-African

trends (9) Various Various Various Various Various Various 0.75 36% 11.8

a�vt is the component of motion of the unacceptable hotspot relative to that predicted from HS3-NUVEL1A in the direction perpendicular to the observed

trend, where �vti = |vpredi | sin(αpred

i ), |vpredi | is the speed predicted from the model, and α

predi is the observed trend minus the predicted trend. The 1-D errors

are calculated using multivariate error analysis.bI is the data importance the unacceptable datum has in a data set consisting of the HS3-NUVEL1A data and the unacceptable datum.c (V0−V )

V0is the percentage volume decrease relative to the HS3-NUVEL1A error ellipsoid, where V0 is the volume of the HS3-NUVEL1A standard error

ellipsoid and V is the volume of the standard error ellipsoid when an unacceptable trend is added to the HS3-NUVEL1A data set.d�χ2 is the increase in χ2

hotspot relative to that of HS3-NUVEL1A (χ2hotspot = 8.0) when an unacceptable trend is added to the HS3-NUVEL1A data set.

eYoung seafloor σwidth = ± 55 km.f NM ≡ ‘not meaningful.’ These statistics could not be meaningfully calculated.Trend misfits and �vt ’s printed in bold differ significantly from zero with ≥95 per cent confidence.

calculated for any data set including the Comores trend. Althoughthe inability to satisfactorily fit these tracks may be partly due totreating Africa as a single plate instead of separate Nubian andSomalian plates (cf. Chu & Gordon 1999), the main difficulties aresurely due to the unreliability of short tracks and possibly to long-lasting volcanism on slow plates.

Even if we added all rejected trend data listed in Table 6, exceptthose from Africa, to the HS3 data set, the volume of the confidenceellipsoid would only decrease by 36 per cent.

On-ridge hotspots. Morgan (1978) and Schouten et al. (1987) pro-posed that some on-ridge hotspots are caused by the channellingof a near-ridge source to the closest point on a nearby spreadingridge. Here we use the model of Schouten et al. (1987), which ex-cludes the ridge-perpendicular component of plate velocity relativeto the hotspots, to predict trends for the Wolf–Darwin lineament ofthe Galapagos and for both Cobb tracks. These predicted trends arecloser to the observed trends (Table 10) than are those predicted

Table 8. Excluded rate observations.

Hotspot (plate): comments Observed time σage Observed rate ±1σ

Volcanoes used interval (Ma) (Myr) (km Myr−1)

Cobb (Pacific): On-ridgeAxial (≡0.0), Cobb, Gluttony, Lust, Sloth active to 5.2 ±1.30 51 ± 19

Galapagos (Nazca): Long-lasting volcanism, no known consistent horizon to dateEcuador, San Salvador, Raibida, Pinzon, Santa Maria, 0.1 to 3.4 ±0.45 84 ± 14

Santa Cruz, Santa Fe, Espanola, San Christobal

Yellowstone (North America): Only 4 volcanoesthird-cycle caldera, second-cycle caldera, 0.6 to 4.3 ±0.96 36 ± 14

first-cycle caldera, Kilgore

from HS3-NUVEL1A. None of these observations differ signifi-cantly from the HS3-NUVEL1A predictions (Table 10) however,and thus the Schouten et al. (1987) model can be neither excludednor confirmed.

HS3-NUVEL1A

Angular velocities

HS3-NUVEL1A describes the motion of 15 assumed-rigid platesrelative to a global set of hotspots over the past several million years(Tables 11 and 12, Fig. 2). The data used to estimate the relative platemotions are averaged over different time intervals. Earthquake focalmechanisms reflect motion averaged over years or decades to tens ofthousands of years, transform faults average motion over hundredsof thousands to millions of years and spreading rates average motionover 3.2 Myr (DeMets et al. 1990, 1994). The volcanoes used to

C© 2002 RAS, GJI, 150, 321–361


Table 9. Influence of some unacceptable rates.

Hotspot HS3-NUVEL1A Observed Rate �var Model including unacceptable rate

Predicted rate misfit Calculated rate I V0−VV0

�χ2

rate ±1σ ±1σ ±95% ±95% ±1σ

km Myr−1 km Myr−1 km Myr−1 km Myr−1 (km Myr−1)

Cobb (PA) 54.7 ± 4.9 51 ± 19 −4 ± 38 −2 ± 40 54.5 ± 4.9 0.06 3% 0.0Galapagos 21.3 ± 5.9 b 84 ± 14 63 ± 30 66 ± 33 30.8 ± 5.6 0.16 10% 17.0Yellowstone 26.8 ± 7.8 b 36 ± 14 9 ± 32 10 ± 31 29.1 ± 7.8 0.01 −1% 0.3rates (3) Various Various Various Various Various 0.23 2% 18.2rates (3) and Various Various Various Various Various 0.98 41% 28.3Non-African trends (9)

Same conventions as in Table 7.a�vr is the component of motion of the unacceptable hotspot relative to that predicted from HS3-NUVEL1A in thedirection parallel to the observed trend, where �vri = robs

i − |vpredi |cos(αpred

i ), which is equivalent to the rate fittingfunction of Chase (1972), and robs

i is the observed volcanic propagation rate. The 1-D errors are calculated usingmultivariate error analysis.bObserved trend was included in the model for this prediction.

estimate trends and rates for HS3-NUVEL1A all have observed agesof 5 Ma or younger. Summing the 5 Myr length of the 0 to 5 Ma timeinterval with the minimum time (≈0.8 Myr) that we estimate it takesa shield volcano to grow indicates that the time interval averaged forHS3-NUVEL1A is ≈5.8 Myr long. Our ‘global’ hotspot data spanonly a hemisphere and consist of eleven segment trends and twovolcanic propagation rates. The segment trends lie on the Pacific,Nazcan, North American and South American plates.

For the angular velocities of both Minster & Jordan (1978) andGripp & Gordon (1990), the motion of the Antarctic, Caribbeanand Eurasian plates relative to the hotspots differed insignificantlyfrom zero. In contrast, the angular velocities of all plates relativeto the hotspots differ significantly from zero (p ≤ 0.008) in HS3-NUVEL1A. The difference is due both to smaller uncertaintiesin HS3-NUVEL1A and to its having greater rotation rates rela-tive to the hotspots. Some plates in HS3-NUVEL1A neverthelessmove slowly relative to the hotspots (Table 12, Fig. 2). The slow-est moving plates are the Juan de Fuca, Antarctic, African andEurasian plates with root-mean-square (rms) velocities of 10, 15,16 and 20 km Myr−1, respectively. The fastest moving plates are thePacific, Philippine, Australian, Cocos, South American and Indianplates with rms velocities of 105, 86, 74, 50, 45 and 45 km Myr−1,respectively. The remaining plates, the North American, Nazca,Scotia, Caribbean and Arabian plates move at 27, 30, 30, 30 and30 km Myr−1, respectively. The Caribbean angular velocity and rmsvelocity are likely to be unreliable because geodetic observationsindicate that the velocity of the Caribbean Plate relative to North

Table 10. Velocity predictions using the Schouten et al. (1987) model for on-ridge hotspots.

Hotspot HS3-NUVEL1A Observed Schouten et al. (1987)b Observedtrend rate

Predicted Predicted ±1σ Predicted Predicted ± 1σ

rate ± σ trend trend rate (km Myr−1)(km Myr−1) ± 1σ (km Myr−1)

Cobb (JdF) 21.3 ± 7.5 034.1 ± 14.6◦ 084.1 ± 45.6◦a 074◦ 35 —Cobb (PA) 55.0 ± 5.0 311.5 ± 8.1◦ 326.9 ± 26.1◦a 326◦ 35 51 ± 19Galapagos (CO) 57.7 ± 6.1 026.1 ± 5.3◦ — 043◦ 33 —Galapagos, Wolf–Darwin (NZ) 20.0 ± 5.9 092.5 ± 15.8◦ 124.5 ± 22.2◦a 149◦ 33 —Louisville, Hollister (PA) 99.6 ± 7.1 294.8 ± 3.3◦ 306 ± 26◦ a 294◦ 39 —

aYoung seafloor σwidth = ±55 km.bSchouten et al. (1987) velocities are predicted using NUVEL-1A for the relative plate velocity at the spreading ridge,using HS3-NUVEL1A for plate velocity relative to the hotspots predicted at the spreading ridge, and assuming thespreading ridge is perpendicular to spreading direction.

America differs significantly from that in NUVEL-1A (Dixon et al.1998).

Plates with large continental area tend to move slower thanoceanic plates, but there is much overlap in the rms velocitieswith, for example, the Juan de Fuca, Scotia, Caribbean and Nazcaplates all moving more slowly than the South American, Indian andAustralian plates (Fig. 3a). Plates with a substantial portion (28–44 per cent) of their boundaries attached to subducting slabs tendto move faster than plates with little (≤9 per cent) or none of theirboundaries attached to subducting slabs (Forsyth & Uyeda 1975),but again with overlap in rms velocities (Fig. 3b). Among the sixplates attached to substantial subducting slabs (Juan de Fuca, Nazca,Cocos, Australia, Philippine and Pacific), the rms velocity tendsto increase with increasing age of the lithosphere being subducted(Carlson et al. 1983) (Fig. 3c). Some of the slowest moving platesmove in surprising directions (Figs 2 and 4). The Antarctic Platemoves slowly but significantly away from the Peru–Chile trench.The African Plate and, to a lesser extent, the Juan de Fuca Platemove obliquely relative to their short trenches. These directions ofmotion may be real, but small systematic errors, especially in ob-served rates and in NUVEL-1A (cf. Gordon et al. 1999), might bet-ter explain these results. In HS3-NUVEL1A the Pacific Plate moves8–9 km Myr−1 faster to the west-northwest than in HS2-NUVEL1(Fig. 4).

As a check on the robustness of our angular velocities, we inves-tigate their sensitivity to the omission of a single datum. Removingany one datum always results in an angular velocity that lies inside

C© 2002 RAS, GJI, 150, 321–361


Table 11. HS3-NUVEL1A active to 5 Ma observed, calculated, and predicted values.

Hotspot Locationa Observed HS3-NUVEL1 calculated values Observed Predicted ValuesTrend trend −

◦N ◦E ± 1σ trend Rate ± 1σ calculated Trend Rate ± 1σ

± 1σ (km Myr−1) trend ± 1σ (km Myr−1)

Easter −27.11 −110.06 098.6 ± 31.7◦b 107.0 ± 9.9◦ 32.7 ± 5.3 −8.4◦ 108.0 ± 10.5◦ 32.5 ± 5.3Galapagos −0.54 −90.83 121.3 ± 40.9◦b 089.9 ± 14.9◦ 21.3 ± 5.9 31.4◦ 084.8 ± 15.9◦ 21.9 ± 6.0Hawaii 20.65 −156.91 303.5 ± 6.3◦ 300.2 ± 4.4◦ 103.3 ± 4.5 3.3◦ 296.5 ± 6.1◦c 103.6 ± 4.6c

Juan Fernandez −33.73 −80.45 086.4 ± 14.0◦ 081.0 ± 9.6◦ 33.8 ± 5.8 5.4◦ 075.4 ± 12.3◦ 36.0 ± 7.0Macdonald −28.31 −142.31 291.0 ± 8.7◦ 292.6 ± 3.1◦ 116.5 ± 6.0 −1.6◦ 292.9 ± 3.3◦ 116.4 ± 6.0Marquesas −9.59 −139.37 310.0 ± 12.3◦ 291.6 ± 3.2◦ 116.5 ± 5.2 18.4◦ 290.2 ± 3.3◦ 116.9 ± 5.2Martin Vaz −20.49 −29.09 264.9 ± 52.7◦ 251.2 ± 9.9◦ 47.2 ± 5.2 13.7◦ 250.6 ± 10.0◦ 47.3 ± 5.2Pitcairn −25.21 −129.59 289.1 ± 35.9◦ 287.9 ± 2.9◦ 117.9 ± 5.6 1.2◦ 287.9 ± 2.9◦ 117.9 ± 5.6Samoa −14.19 −170.74 283.2 ± 11.2◦ 298.5 ± 3.8◦ 116.8 ± 5.9 −15.3◦ 300.6 ± 4.0◦ 117.4 ± 5.8Society −17.33 −149.95 292.6 ± 7.8◦ 294.5 ± 3.3◦ 117.9 ± 5.6 −1.9◦ 295.0 ± 3.7◦d 117.9 ± 5.6d

Yellowstone 44.38 −111.05 241.0 ± 23.8◦ 249.5 ± 10.7◦ 26.8 ± 7.8 −8.5◦ 251.8 ± 12.0◦ 26.9 ± 7.9

aLocation = centre of moment of volcano locations. It is a by-product of the solution for best-fit pole to the volcano locations.bYoung seafloor σwidth = ± 55 km.cHawaiian rate included in prediction.d Society rate included in prediction.Hotspot Observed HS3-NUVEL1A Observed Predicted values Predicted values

rate Calculated rate − (rate removed) (rate and trend removed)±1σ rate ±1σ calculated

(km Myr−1) (km Myr−1) rate Rate ±1σ Trend Rate ±1σ Trend(km Myr−1) (km Myr−1) ±1σ (km Myr−1) ±1σ

Hawaii 108 ± 5 103.3 ± 4.5 5 92.2 ± 8.5e 300.7 ± 4.4◦e 92.5 ± 8.9 298.0 ± 6.2◦Society 106 ± 9 117.9 ± 5.6 −12 125.1 ± 6.2 f 294.6 ±3.2◦ f 125.1 ± 6.2 295.0 ± 3.6◦eHawaiian trend included in prediction.f Society trend included in prediction.

Table 12. Angular velocities of HS3-NUVEL1A.

Plate Angular Velocity Approx. Standard Error Ellipse σω p(χ2(ωH S3 − 0))b

Rms Speed p(χ2(ωH S3 − ωH S2))c

◦ Myr−1 km Myr−1◦N ◦E ◦Myr−1 σmax σmin ζ a

max

Africa −43.386 21.136 0.1987 28.05◦ 15.02◦ 052◦ 0.0585 8 × 10−3 15.9 3%Antarctica −47.339 74.514 0.2024 26.61◦ 17.64◦ 006◦ 0.0569 1 × 10−3 15.0 5%Arabia 2.951 23.175 0.5083 10.63◦ 7.37◦ 058◦ 0.0611 2 × 10−20 30.3 2%Australia −0.091 44.482 0.7467 6.73◦ 4.35◦ 043◦ 0.0704 4 × 10−28 73.8 2%Caribbean −73.212 25.925 0.2827 20.79◦ 11.81◦ 045◦ 0.0543 1 × 10−6 30.1 4%Cocos 13.171 −116.997 1.1621 4.32◦ 2.69◦ 149◦ 0.0714 <1 × 10−43 50.3 5 × 10−3

Eurasia −61.901 73.474 0.2047 27.38◦ 17.52◦ 003◦ 0.0524 4 × 10−4 20.0 5%India 3.069 26.467 0.5211 10.22◦ 7.08◦ 056◦ 0.0628 3 × 10−20 45.0 2%Juan da Fuca −39.211 61.633 1.0122 5.58◦ 3.33◦ 021◦ 0.0618 <1 × 10−43 10.3 15%Nazca 35.879 −90.913 0.3231 16.51◦ 12.26◦ 004◦ 0.0583 1 × 10−9 29.6 9 × 10−3

North America −74.705 13.400 0.3835 15.59◦ 8.70◦ 056◦ 0.0548 1 × 10−11 26.9 6%Pacific −61.467 90.326 1.0613 5.71◦ 3.69◦ 166◦ 0.0498 <1 × 10−43 105.4 32%Philippine −53.880 −16.668 1.1543 5.26◦ 2.64◦ 081◦ 0.0581 <1 × 10−43 85.5 8%Scotia −76.912 52.228 0.4451 13.56◦ 7.99◦ 019◦ 0.0523 6 × 10−18 29.9 —South America −70.583 80.401 0.4358 13.82◦ 8.59◦ 174◦ 0.0503 4 × 10−19 45.3 8%NNR-NUVEL1A −55.908 69.930 0.4359 13.48◦ 8.28◦ 008◦ 0.0545 8 × 10−17 — —

aζmax is the azimuth of the major axis of the error-ellipse.bp(χ2(ωH S3 − 0) is the probability of obtaining data as different or more different as those used herein if the angular velocity of the plate is zero.cp(χ2(ωH S3 − ωH S2) is the probability of obtaining data as different or more different as those used in HS3-NUVEL1A if the angular velocity of the plate isthat of HS2-NUVEL1.Probabilities of ≤5% are printed in bold.The HS3-NUVEL1A covariance matrix in Cartesian coordinates and in units of 10−10 radians2 Myr−2 is σ 2

x σ 2yx σ 2

zx

σ 2xy σ 2

y σ 2zy

σ 2xz σ 2

yz σ 2z

=

7662 3518 −1782

3518 15615 3094−1782 3094 8553

.

C© 2002 RAS, GJI, 150, 321–361


Figure 2. Contour map of plate speed relative to the hotspots for the HS3-NUVEL1A angular velocities. Thick dashed lines mark equators to poles of theangular velocities.Thin dashed lines delimit where plate speed differs from zero at the 95 per cent confidence level. Filled circles mark pole (or antipole) locationsif pole (or antipole) lies on its own plate. Medium solid lines are the approximate plate boundaries. (a) Mercator projection. (b) Stereographic projection aboutnorth pole. (c) Stereographic projection about south pole.

the 95 per cent confidence ellipsoid of HS3-NUVEL1A. The omis-sion of the Hawaiian rate has the most significant effect (p = 0.10whereas p ≥ 0.34 for all other cases). Thus the set of angular veloc-ities appears to be robust.

If the rates are omitted, a set of angular velocities can be esti-mated from the trend-only data set, which has an uncertainty of thecomponent in angular velocity parallel to the Pacific-hotspot pole

that is ±0.62 deg Myr−1 (95 per cent confidence), which is six timesgreater than that for HS3-NUVEL1A.

Net-rotation of the lithosphere

NNR-NUVEL1A is a set of angular velocities, consistent with theNUVEL-1A relative plate velocities, of the plates in a reference

C© 2002 RAS, GJI, 150, 321–361


Figure 3. Plate parameter plotted against rms velocity. Filled triangles show velocities from HS3-NUVEL1A; open squares show velocities from HS2-NUVEL1.(a) The percentage of the plate area that is continental, as defined by the 2-km-deep contour, is plotted against rms velocity. (b) The approximate percentageof plate boundary that is attached to a subducting slab (based on the subduction zones marked in Fig. 4) is plotted against rms velocity. (c) The approximaterange of the age of the seafloor about to be subducted (read off of map of Mueller et al. (1996), except that of Africa, which is from Jarrard (1986), and that ofEurasia, which was read off of the map of Cande et al. (1989)) is plotted against rms velocity. Symbol size increases with increasing percentage of boundaryattached to a slab.

frame in which there is no net rotation of the lithosphere(Argus & Gordon 1991; DeMets et al. 1994). The uncertainty ofthe angular velocity of a plate relative to the no-net-rotation ref-erence frame (Gripp 1994) is small relative to the uncertainty ofthe angular velocity of the same plate relative to the hotspots. Itis thus neglected below. The angular velocity of any plate rela-tive to the NNR-NUVEL1A no-net-rotation reference frame dif-fers significantly from the corresponding angular velocity rela-tive to the hotspots specified in HS3-NUVEL1A (p = 8 × 10−17)(Table 12). Thus, the lithosphere has a net rotation relative tothe hotspots of 0.44 ±0.11 deg Myr−1 (95 per cent confidencelevel here and below) about a pole of 56◦S, 70◦E, faster than the

net rotation (0.33 ± 0.17 deg Myr−1) for HS2-NUVEL1 (Argus &Gordon 1991). The newly determined net rotation can be comparedwith predictions from models for plate driving forces. For example,Cocksworth (1995) used the NUVEL-1 relative plate motions asobservables to invert for the relative contribution of plate drivingforces. He predicted that the net rotation of the lithosphere rela-tive to the deep mantle should be 0.252 deg Myr−1 about 59◦S,48◦E (after a small correction to bring the prediction to consistencywith NUVEL-1A). This prediction lies outside the 3-D 95 per centconfidence region (p = 4 × 10−4), but the predicted pole does lieinside the 2-D 95 per cent confidence ellipsoid for the pole location.The statistical significance of the net rotation depends critically on

C© 2002 RAS, GJI, 150, 321–361


Figure 4. Plate velocities relative to the hotspots. Each arrow shows the displacement path of a point on a plate if the plate were to maintain its currentangular velocity relative to the hotspots for 40 Myr. Ellipses show the 2-D 95 per cent confidence ellipse of velocity multiplied by 40 Myr. Thick arrows withthick confidence ellipses are determined from the HS3-NUVEL1A angular velocities. Thin arrows with dotted confidence ellipses are determined from theHS2-NUVEL1 angular velocities. Filled circles show the pole (or antipole) locations if the pole (or antipole) lies on its own plate; stippled circles show those forHS2-NUVEL1 and black circles show those for HS3-NUVEL1A. Medium solid lines are the approximate plate boundaries. Barbed lines show the approximatelocation of subduction zones with barbs on the overthrust plate. (a) Mercator projection. (b) Lambert’s azimuthal equal area projection about north pole.(c) Lambert’s azimuthal equal area projection about south pole.

the inclusion of volcanic propagation rates. Its magnitude would be0.41 ± 0.61 deg Myr−1 if the rates were excluded.

C O M PA R I S O N W I T H P R I O R R E S U LT S

Uncertainties in, and information content of,trends and rates

For the HS3 data set, trend standard errors on the Pacific Platerange from±6.3◦ for 600-km-long Hawaii to±35.9◦ for 90-km-long

Pitcairn (Table 3). In contrast, prior data sets have Pacific Platestandard errors ranging from ±10◦ to ±20◦ (Table 13). For the HS3data set, trend standard errors on the Nazca Plate range from ±14.0◦

for Juan Fernandez to ±40.9◦ for Galapagos. This compares with±10◦ to ±20◦ in prior data sets. Relative to previously assigneduncertainties, our length-dependent trend uncertainties lead to thefollowing:

(1) a greater variation in assigned standard errors

C© 2002 RAS, GJI, 150, 321–361


Table 13. Trend uncertainties and data importance for a selection of models of current plate motion relative to the hotspots.

Plate Hotspot HS3-NUVEL1A Ricard et al. (1991) Pollitz (1986) Minster & Jordan (1978) Minster et al. (1974)

σtrend Ib σtrend Ib σtrend Ib σtrend Ib σtrend Ib

AF Ascension — — ± 10◦ 0.60 — — — — ± 20◦ 0.07AF Bouvet — — — — — — — — ± 10◦ 0.31AF Comores ± 34.0◦ NMc — — — — — — — —AF Reunion ± 15.8◦ 1.00 ± 10◦ 0.77 — — — — ± 10◦ 0.54AF St. Peter and Paul’s rocks — — — — — — — — ± 30◦ 0.04AF Tristan da Cuhna — — ± 20◦ 0.17 — — — — ± 20◦ 0.06AN Kerguelen — — — — — — — — ± 20◦ 0.29AN Prince Edward — — — — — — — — ± 20◦ 0.84AU Lord Howe ± 10.6◦ 0.18 — — — — — — — —AU Tasmantid ± 8.9◦ 0.22 — — — — — — — —CO Galapagos — — ± 10◦ 0.11 — — ± 10◦ 0.17 ± 10◦ 0.02EU Iceland — — — — — — — — ± 30◦ 0.08JF Cobb ± 45.6◦d 0.08 — — — — — —NA Iceland — — ± 30◦ 0.18 — — — — ± 20◦ 0.14◦NA Raton — — — — — — — — ± 30◦ 0.02NA Yellowstone ± 23.8◦ 0.20 ± 20◦ 0.35 — — ± 20◦ 0.46 ± 20◦ 0.04NZ Easter ± 31.7◦d 0.10 — — — — — — ± 20◦ 0.00NZ Galapagos ± 40.9◦d 0.13 ± 10◦ 0.20 ± 14.0◦ 0.36 ± 10◦ 0.48 ± 10◦ 0.02NZ Juan Fernandez ± 14.0◦ 0.47 — — ± 15.0◦ 0.24 — — — —PA Bowie ± 22.3◦ 0.15 — — — — — — — —PA Cobb ± 26.1◦ 0.09 ± 15 0.03 — — ± 15◦ 0.39 ± 20◦ 0.01◦PA Easter — — — — — — — — ± 20◦ 0.00PA Eastern Caroline ± 6.8◦ 0.27 — — ± 10.0◦ 0.18 — — — —PA Hawaii ± 6.3◦ 0.49 ± 10◦ 0.02 ± 10.0◦ 0.15 ± 10◦ 0.29 ± 10◦ 0.01PA Islas Revillagigedo ± 14.5◦d 0.06 — — — — — — — —PA Louisville (off-ridge) ± 34.8◦ 0.01 — — — — — — — —PA Louisville (on-ridge) ± 26◦d 0.02 — — — — — — — —PA Macdonald ± 8.7◦ 0.13 ± 15◦ 0.02 ± 10.0◦ 0.06 ± 15◦ 0.07 ± 10◦ 0.02PA Marquesas ± 12.3◦ 0.07 ± 15◦ 0.01 — — ± 15◦ 0.08 — —PA Pitcairn ± 35.9◦ 0.01 ± 15◦ 0.02 ± 10.0◦ 0.06 ± 15◦ 0.06 — —PA Samoa ± 11.2◦ 0.12 — — — — — — — —PA Society ± 7.8◦ 0.18 ± 15◦ 0.01 ± 10.0◦ 0.06 ± 15◦ 0.08 — —SA Martin Vaz ± 52.7◦ 0.04 — — — — — — ± 10◦ 0.45SA Tristan da Cuhna — — ± 30◦ 0.15 — — — — ± 30◦ 0.04

AF Sum of AF trends — — Various 1.54 — — — — Various 1.02AN Sum of AN trends — — — — — — — — Various 1.13CO Sum of CO trends — — Various 0.11 — — Various 0.17 Various 0.02EU Sum of EUtrends — — — — — — — — Various 0.08NA Sum of NA trends Various 0.20 Various 0.53 — — Various 0.46 Various 0.20NZ Sum of NZ trends Various 0.70 Various 0.20 Various 0.60 Various 0.48 Various 0.02PA Sum of PA trends Various 1.00 Various 0.11 Various 0.51 Various 0.97 Various 0.04SA Sum of SA trends Various 0.04 Various 0.15 — — — — Various 0.49

Sum of non-PA trends Various 0.94 Various 2.53 Various 0.60 Various 1.11 Various 2.96

aBold hotspots were used in HS3-NUVEL1A.bI is data importance. A data importance in bold is the data importance the trend has in HS3-NUVEL1A. A data importance in italics is the dataimportance the trend would have had in HS3-NUVEL1A if it had not been excluded from that data set. Data importances were not published in Pollitz(1986) and Ricard et al. (1991), but were calculated herein.cNM = ‘not meaningful.’ Importance could not be meaningfully calculated.d Young seafloor width standard error is ±55 km.

(2) smaller uncertainties for the trends on the Pacific Plate, es-pecially for the Hawaiian trend, and

(3) larger uncertainties for the trends on other (less fast moving)plates (Table 13).

Our results indicate that the uncertainties assigned to trends for theslow-moving plates in prior work were too small and in some priordata sets unrealistically small (cf. Ricard et al. 1991) (Table 13). Therates in HS3 have a total data importance of 1.1 (Table 14).

The greater weighting given herein to Pacific Plate trends seemsappropriate. For a hotspot segment to have a discernible trend, its

length should be at least twice its width. The ±1σ width of atypical hotspot track is 66 km (equal to twice the standard devi-ation). Thus a discernible trend requires a length of ≈130 km ormore. For the fastest moving plate, the Pacific Plate, which moves≈100 km Myr−1, it takes 1.3 Myr to build a track this long. For aplate with the median plate speed (30 km Myr−1), it takes 4.3 Myr.For a slow moving plate (10–20 km Myr−1), it takes 6.5 to 13 Myr.Thus, useful hotspot tracks for the HS3-NUVEL1A set of angularvelocities with its ≈5.8 Myr duration come dominantly from thefastest-moving plate (the Pacific Plate), with less useful tracks fromplates moving at about the median speed (South American, Nazcan

C© 2002 RAS, GJI, 150, 321–361


Table 14. Rate uncertainties and data importance for a selection of models of current plate motion relative to the hotspots.

Plate Hotspot HS3-NUVEL1A Ricard et al. (1991) Pollitz (1986) (Minster & Jordan 1978) Minster et al. (1974)

σrate Ib σrate Ib σrate Ib σrate Ib σrate Ib

(km Myr−1) (km Myr−1) (km Myr−1) (km Myr−1) (km Myr−1)

NA Yellowstone ±14 0.01 — — — — — — — —NZ Galapagos ±14 0.16 — — — — — — — —PA Bowie — — — — ±4.0 0.75 — — — —PA Cobb ±19 0.06 — — — — — — — —PA Hawaii ±5 0.74 ±20 0.09 ±2.5 0.81 ±20 0.14 — —PA Macdonald — — ±20 0.05 ±15.6 0.08 ±20 0.24 — —PA Marquesas — — ±20 0.09 ±17.5 0.04 ±20 0.20 — —PA Pitcairn — — ±20 0.04 — — ±30 0.10 — —PA Society ±9 0.34 ±20 0.08 ±9.7 0.20 ± 20 0.22 — —PA Sum of PA rates Various 1.08 Various 0.35 Various 1.88 Various 0.90 — —

Same conventions as Table 13.

and North American plates) and no useful tracks from slow-movingplates.

Differences between HS3-NUVEL1A and HS2-NUVEL1

The volume of the 3-D error ellipsoid of HS3-NUVEL1A is abouthalf that of HS2-NUVEL1. Nine of fourteen of the HS2-NUVEL1angular velocities lie outside the 95 per cent confidence region of thecorresponding HS3-NUVEL1A angular velocity (Table 12). How-ever, all fourteen of the HS3-NUVEL1A angular velocities (withcounterparts in HS2-NUVEL1) lie inside the 95 per cent confi-dence region of the corresponding HS2-NUVEL1 angular velocity.The vector difference between the angular velocity of a plate rela-tive to the hotspots in HS3-NUVEL1A and its counterpart in HS2-NUVEL1 varies from plate to plate. The largest difference (a vectorwith a length of 0.17 deg Myr−1) is for the Cocos Plate, which isstatistically significant (p = 5 × 10−3) and the smallest difference(0.08 deg Myr−1) is for the Pacific Plate, which is statistically in-significant (p = 0.32) (Fig. 4, Table 12).

These changes can be thought of as having two components. Thefirst component is the change in assumed relative angular velocities.The change in vector length of an angular velocity relative to thePacific Plate in NUVEL-1 and the corresponding angular velocityin NUVEL-1A varies from a high of 0.09 deg Myr−1 for the CocosPlate to a low of 0.02 deg Myr−1 for the Juan de Fuca Plate. Thesecond component is the change of the Pacific Plate angular velocitybetween HS2-NUVEL1 and HS3-NUVEL1A, which may be causedby several factors including the following:

(1) Volcanic propagation rates were fit by the Chase (1972) ratefitting function in determining HS2-NUVEL1, but by the Minsteret al. (1974) fitting function in determining HS3-NUVEL1A.

(2) The set of relative plate angular velocities was changedfrom the NUVEL-1 angular velocities in HS2-NUVEL1 to the(4.38 per cent) smaller NUVEL-1A angular velocities in HS3-NUVEL1A.

(3) The data set of volcano trends and propagation rates, alongwith their assigned uncertainties, was revised.

Numerical experiments indicate that the third factor, the revi-sions to the volcanic trends, propagation rates and their associateduncertainties has an effect many times greater than the other twofactors. The size of the effect of the third factor is indicated by twonumerical experiments. First, we combine the HS3 data set with the

NUVEL-1 angular velocities using the Chase rate fitting functionand compare it with HS2-NUVEL1 (which was determined usingthe Chase rate fitting function). The resulting Pacific-hotspot rate ofrotation is 0.08 deg Myr−1 higher, and the calculated rate at Hawaiiis 9 km Myr−1 higher, than in HS2-NUVEL1. Second, we com-bine the HS2 data set with the NUVEL-1A angular velocities usingthe Minster et al. (1974) fitting function to compare it with HS3-NUVEL1A (which was determined using the Minster et al. (1974)rate fitting function). The resulting Pacific-hotspot rate of rotationis 0.11 deg Myr−1 lower, and the calculated rate at Hawaii is 12 kmMyr−1 lower, than in HS3-NUVEL1A. These changes are as largeor larger than those between HS2-NUVEL1 and HS3-NUVEL1A.

Many changes to the data contribute to the speed up of the esti-mated Pacific Plate angular velocity. A key change, however, is thechange between HS2 and HS3 data sets of the observed Hawaiianrate and its uncertainty. In HS2, the observed Hawaiian rate is100 ± 20 km Myr−1 (±1σ ), whereas in HS3, it is 108 ± 5 km Myr−1

(±1σ ). Making this single change to the HS2-NUVEL1 data setwould produce an increase in the estimated Pacific Plate rate of ro-tation of 0.09 deg Myr−1 and increase the calculated rate at Hawaiiby 10 km Myr−1, which is more than sufficient to account for theentire change in Pacific Plate rotation rate between HS2-NUVEL1and HS3-NUVEL1A.

Pacific Plate angular velocity

The Pacific Plate hotspot angular velocities estimated by Minster& Jordan (1978), Pollitz (1986) and Gripp & Gordon (1990) (bothfor NUVEL-1 and rescaled to NUVEL-1A) all lie within the 95 percent confidence ellipsoid of HS3-NUVEL1A (Table 15, Fig. 5).Perhaps surprisingly, the recent estimate by Wessel & Kroenke(1997) lies far outside the 95 per cent confidence ellipsoid of HS3-NUVEL1A (p < 10−41). Their pole of rotation lies 55◦ from thatof HS3-NUVEL1A and their rotation rate is 0.14 deg Myr−1 faster(Fig. 5). The length of the vector difference between their angularvelocity and the Pacific Plate angular velocity of HS3-NUVEL1Aexceeds the length of the latter (Table 15). Wessel & Kroenke’s(1997) pole is so different from that of HS3-NUVEL1A becausetheir estimate is heavily weighted towards fitting the active to 3 Matrend of Hawaii at the cost of poorly fitting nearly all other hotspottrends that we use. Fig. 6 shows that their angular velocity predictsdirections of motion that have a median misfit to the trends of otherchains of ≈50◦, which is huge by any standard.

C© 2002 RAS, GJI, 150, 321–361


Table 15. Other estimates of the angular velocity of the Pacific plate relative to the hotspots.

Model Instant Pacific relative to hotspots = ω |ωH S3 − ω| |ωH S3T − ω|or p(χ2(�ω))c

Finitea ◦N ◦E deg Myr−1 deg Myr−1 p(χ2(�ω))c

active to 5 Ma HS3-NUVEL1A Instant −61.467 90.326 1.0613 – – 96%active to 5 Ma trend-only, HS3T-NUVEL1A Instant −60.517 87.556 1.0273 0.0453 74% –NNR-NUVEL1A (Argus & Gordon 1991) Instant −63.037 107.360 0.6411 0.4359 8 × 10−17 29%0–1 Ma Epp (1978) Finite −36 104 0.84 0.51 4 × 10−16 2 × 10−9

0–3 Ma Wessel & Kroenke (1997) Finite −25.00 153.00 1.2 1.1 <10−43 <10−43

0–3 Ma Petronotis & Gordon (1999) Finite −61.000 85.000 1.000 0.077 25% 97%0-(3.2–5) Ma Pollitz (1986) Instant −61 85 0.99 0.09 18% 97%0–4 Ma Harada & Hamano (2000) Finite −40.90 75.20 0.9006 0.4142 3 × 10−15 3 × 10−5

0–5 Ma Petronotis & Gordon (1999) Finite 61.700 97.200 0.960 0.117 23% 58%0–10 Ma AM1-2 (Minster & Jordan 1978) Instant −61.66 97.19 0.967 0.111 28% 57%0–10 Ma HS2-NUVEL1 (Gripp & Gordon 1990) Instant −60.2 90.0 0.98 0.08 32% 98%0–10 Ma HS2-NUVEL1 trend-only Instant −61.0 92.7 0.88 0.18 2 × 10−3 91%0–10 Ma HS2-NUVEL1A Instant −59.918 89.687 0.9465 0.1181 7% 98%0-(up to 10’s of Ma) AM1 Minster et al. (1974) Instant −67.3 120.6 0.83 0.33 3 × 10−6 7 × 10−3

0-(up to 10’s of Ma) Ricard et al. (1991) Instant −62 102 0.79 0.29 7 × 10−7 41%1–15 Ma Epp (1978) Finite −65 140 0.86 0.42 4 × 10−9 7 × 10−7

3.0–15.1 Ma Wessel & Kroenke (1997) Finite −71.00 92.50 1.09 0.18 10% 4%5–20 Ma Petronotis & Gordon (1999) Finite −69.754 109.527 0.950 0.228 1% 2%0–18 Ma Fleitout & Moriceau (1992) Finite −72.15 101.87 0.802 0.32 7 × 10−8 12%0–20 Ma Petronotis & Gordon (1999) Finite −68.000 105.000 0.950 0.193 4% 9%0–20 Ma Harada & Hamano (2000) Finite −64.00 83.50 0.8220 0.2481 2 × 10−7 71%0–25 Ma Lonsdale (1988) Finite −75 120 0.88 0.34 7 × 10−6 2 × 10−3

19.9–43.1 Ma Wessel & Kroenke (1997) Finite −57.17 117.52 0.53 b 0.56 2 × 10−27 5%20–43 Ma Petronotis & Gordon (1999) Finite −55.431 132.455 0.526 b 0.609 4 × 10−29 2 × 10−3

23–42 Ma Epp (1978) Finite −59 126 0.4 b 0.7 2 × 10−43 6%24–43 Ma Fleitout & Moriceau (1992) Finite −54 122 0.643 b 0.494 4 × 10−18 1 × 10−3

0–42 Ma Duncan & Clague (1985) Finite −68.0 105.0 0.72 b 0.37 2 × 10−11 29%0–43 Ma Watts et al. (1988) Finite −65 120 0.70 b 0.41 1 × 10−12 3%0–43 Ma Fleitout & Moriceau (1992) Finite −66.09 119.37 0.724 b 0.395 3 × 10−11 3%0–43 Ma Petronotis & Gordon (1999) Finite −64.200 121.600 0.698 b 0.422 6 × 10−13 2%0–42 Ma Harada & Hamano (2000) Finite −65.80 110.20 0.6630 b 0.4232 3 × 10−15 22%

aInstant/Finite refers to whether the model is an instantaneous velocity or finite displacement solution. Finite rotations were approximated asangular velocities by dividing the rotation angle by the given duration of the time interval, except for models including the Hawaiian-Emperorbend, which was rescaled to 47 Ma (see below).bRotation rate rescaled to a 47 Ma Hawaii-Emperor bend (Sharp & Clague 1999).c p(χ2

ν (�ω)) is the probability of obtaining the data as different or more different as the data used herein if the predictions of the specifiedangular velocity are true.Probabilities of ≤5% are printed in bold.The covariance matrix of the active to 5 Ma trend-only (HS3T-NUVEL1A) set of angular velocities in Cartesian coordinates and in units of10−10 radians2 Myr−2 is σ 2

x σ 2yx σ 2

zx

σ 2xy σ 2

y σ 2zy

σ 2xz σ 2

yz σ 2z

=

10221 13820 −18498

13820 98021 −132363−18498 −132363 225893

.

M O T I O N B E T W E E N H O T S P O T S

Our angular velocities are estimated assuming that the hotspots arefixed with respect to one another. This assumption is, at best, anapproximation, but one that allows us to formulate and to quantita-tively test a variety of hypotheses.

Active to 5.0 Ma (HS3 time interval)

The difference between each observed trend (or rate) and the sametrend (or rate) predicted from a set of angular velocities, determinedafter the removal of that one trend (or rate), provides a way to ex-amine how well each datum agrees with the rest of the data. Nodatum is misfit outside the combined 95 per cent confidence limitof the predicted and observed trend (or rate) (Table 16, column

4). The misfits, when expressed as a component of velocity rela-tive to the other hotspots, range from a low of 3 ± 145 km Myr−1

(95 per cent confidence limit here and below) for Pitcairn to ahigh of 40 ± 48 km Myr−1 for Marquesas (Table 16, column 9).The least uncertain component of motion between hotspots cor-responds to the Hawaiian rate, 16 ± 19 km Myr−1 parallel to itsobserved trend. The most uncertain component of motion betweenhotspots corresponds to the Pitcairn trend, 3 ± 145 km Myr−1 per-pendicular to its observed trend. Typical uncertainties are ±20 to±40 km Myr−1, which reflect the resolution of our data and re-sulting model. Thus our finding of insignificant motion betweenhotspots is not inconsistent with the 10–20 km Myr−1 motionfound by Molnar & Stock (1987) between the Hawaiian hotspotand the hotspots in the Atlantic and Indian oceans over the past50–65 Myr.

C© 2002 RAS, GJI, 150, 321–361


Four 4-Myr-long time intervals

We also repeated these same tests for four data sets with 4 Myrdurations: active to 3.2 Ma, 0.0 to 4.0 Ma, 1.0 to 5.0 Ma and 2.0to 6.0 Ma. For the resulting four global models, χ2

hotspot indicatesconsistency with the assumption of fixed hotspots (0.09 ≤ p ≤ 0.76;Table 17).

For each of the four data sets, the difference between each ob-served trend (or rate) and the same trend (or rate) predicted from aset of angular velocities, determined after the removal of that onetrend (or rate), was examined. Out of the 43 possible tests, two in-dicated significant motion: the Hawaiian trend for 2.0 to 6.0 Maand the Marquesas trend for 2.0 to 6.0 Ma (Table 17). Because weused the 95 per cent confidence level, for each individual test thereis a 5% chance of wrongly concluding that the null hypothesis (i.e.that there is no significant motion between hotspots) is false whenit is in fact true. Given that we employed this test 43 times, the ex-pected number of false positives is two, which is consistent with thetwo positives that we find. Thus, these results give no evidence formotion between hotspots.

C H A N G E I N PA C I F I C P L AT E M O T I O NR E L AT I V E T O T H E H O T S P O T S

Hawaii versus the rest of the globe

Interpretation of recent changes in plate motion are very stronglyinfluenced by the alignment of young volcanoes in the Hawaiianchain (Epp 1978; Cox & Engebretson 1985; Engebretson et al. 1985;Pollitz 1986; Wessel & Kroenke 1997). Here we use sets of hotspotrates and trends to test the consistency between the Hawaiian trackand tracks from the rest of the globe. Specifically we examine thetrend of the Hawaiian track over four overlapping 4-Myr-long inter-vals, 2.0 to 6.0 Ma, 1.0 to 5.0 Ma, 0.0 to 4.0 Ma and active to 3.2 Ma,for which the observed Hawaiian trend respectively is 278◦ ± 15◦,293◦ ± 9◦, 302◦ ± 8◦ and 314◦ ± 9◦ (±1σ ). Thus, between the 2.0 to6.0 Ma and the active to 3.2 Ma time intervals, the observed Hawai-ian trend rotates 36◦ ± 17◦ (±1σ ) clockwise (CW) (Table 17). Wecompare this with the trend of Hawaii predicted from the rest of theglobal data for the same four time intervals, for which the predictedHawaiian trend respectively is 315◦ ± 10◦, 312◦ ± 9◦, 294◦ ± 8◦ and290◦ ± 8◦ (±1σ ). Thus, while the observed trend rotates 36◦ ± 17◦

clockwise, the predicted trend rotates 25◦ ± 13◦ anticlockwise. Thedifference between observed and predicted trends progresses overthe same four time intervals as follows: −38◦ ± 35◦ CW, −19◦ ± 24◦

CW, +8◦ ± 22◦ CW and +24◦ ± 24◦ CW (95 per cent confidencelimits). Thus, during the past few millions years, the Hawaiian trendis clockwise of that predicted from the rest of the global hotspottracks, but insignificantly so. For the prior few millions years, theHawaiian trend is anticlockwise of that predicted and the differenceis insignificant or barely significant, depending on the precise timeinterval considered. These results suggest that the change in trendover the past ≈6 Myr is local to the Hawaiian track and probablywithin its uncertainty given the observed width of hotspot tracks.These results are not inconsistent, however, with interpretations thatpostulate a change in Pacific hotspot motion at or before 5 Ma (Cox& Engebretson 1985; Engebretson et al. 1985; Pollitz 1986; Candeet al. 1995), but contradict interpretations that place the change atabout 3 Ma (Harbert & Cox 1989; Wessel & Kroenke 1997). Theessential conclusion is that great caution should be exercised in in-terpreting changes in plate motion based on the short-term changesin trend along a single hotspot track.

Figure 5. Pole locations for the motion of the hotspots relative to the PacificPlate for angular velocities and finite rotations selected from Table 15. Opentriangle is the angular velocity from HS3-NUVEL1A; the shaded ellipsoidis its 2-D 95 per cent confidence ellipsoid from linear propagation of errorsand the dashed line is its 2-D 95 per cent confidence limit from exact errorpropagation. Solid triangles show estimated poles of current plate motionrelative to the hotspots (P, Pollitz (1986); HS2, Gripp & Gordon (1990); MJ,Minster & Jordan (1978); M+, Minster et al. (1974); WK, Wessel & Kroenke(1997)). Open squares mark poles of finite rotations with time intervals of0 to 47 Ma selected from Table 15 (PG, Petronotis & Gordon (1999); W+,Watts et al. (1988); JC, Jarrard & Clague (1977)).

The Marquesas chain, which lies on the same plate, makes aninteresting contrast with Hawaii. Its length is only 360 km, which isshorter than the length used to estimate three of the four Hawaiiantrends. During the 2.0 to 6.0 Ma time interval, the 360-km-longobserved Marquesas trend is 44◦ ± 26◦ CW of the predicted trend.This clockwise misfit of the Marquesas hotspot track relative to otherhotspots is coeval with the anticlockwise misfit of the Hawaiian trackrelative to the other hotspots.

Late Miocene change in Pacific hotspot motion

The most recent clearly resolvable change in Pacific–Antarctic mo-tion occurred at 6–8 Ma (Cande et al. 1995; Atwater & Stock 1998).Was this change accompanied by a resolvable change in the velocityof the Pacific Plate relative to the hotspots?

Because appropriate error estimates are unavailable for finite ro-tations of the Pacific Plate relative to the hotspots, the most onecan determine is whether a past pole and rate of rotation lie insidethe HS3-NUVEL1A 95 per cent confidence ellipsoid (Table 15).All finite rotations describing Pacific hotspot motion along the en-tire Hawaiian Ridge lie outside the 95 per cent confidence ellip-soid of HS3-NUVEL1A when approximated as an angular velocitythat has stayed fixed in orientation for tens of millions of years(p ≤ 2 × 10−11) (Table 15; Fig. 5). The differences in rotation rateare large, with the HS3-NUVEL1A rate of 1.06 deg Myr−1 being, forexample, approximately 50 per cent faster than the average rotationrate since 47 Ma of the Pacific hotspot rotations of Watts et al. (1988)or of Petronotis & Gordon (1999). On the other hand, the poles of

C© 2002 RAS, GJI, 150, 321–361


Figure 6. Misfit to plate motion data. Left column: misfits to rates or trends. Right column: squared weighted misfit (square of the ratio of the misfit to itsassigned 1σ error). Data from active to 5 Ma are compared with (1) values predicted by the Pacific-hotspot angular velocity of Wessel & Kroenke (1997) (solidblack bar) combined with the relative plate velocities of NUVEL-1A and (2) values calculated from the angular velocities of HS3-NUVEL1A (open triangleand thin lines). Data from active to 3 Ma are compared with (1) values predicted from the Pacific hotspot angular velocity of Wessel & Kroenke (1997) (stippledbar) combined with the relative plate velocities of NUVEL-1A and (2) values calculated angular velocities fit herein to these data (open circles and thin lines).Wessel & Kroenke’s angular velocity poorly fits the active to 5 Ma data, with huge (3 to 6 σ ) misfits to half a dozen observations. In contrast, HS3-NUVEL1Afits all the active to 5 Ma data within their uncertainties. Wessel & Kroenke’s angular velocity also poorly fits the active to 3.2 Ma data, with huge (3 to 6 σ )misfits to three observations. Not only are the non-Hawaiian Pacific trends poorly fit, with the Society, Pitcairn and Samoa trends each being misfit by 50◦,but so are non-Pacific trends, with the Yellowstone trend being misfit by more than 100◦ and Martin Vaz being misfit by 50◦. In contrast, the angular velocityestimated herein fits all the active to 3.2 Ma data within their uncertainties.

rotation for 0–47 Ma lie near the edge of the 95 per cent confidenceregion for the current pole of rotation (Fig. 5). These 0–47 Ma poleslie outside the confidence region, but if and when their uncertaintiesare estimated, we think it is unlikely that the 0–47 Ma poles will proveto differ significantly from the current pole of rotation. Thus, no sta-tistically significant change in direction is resolvable from only thehotspot tracks, although there is other evidence to support a changein direction of motion at 6–8 Ma (Engebretson et al. 1985; Cox& Engebretson 1985; Cande et al. 1995; Atwater & Stock 1998).The volcanic propagation rates strongly indicate, however, that thePacific Plate has sped up relative to the hotspots sometime in thepast 47 Myr.

S H O RT - T E R M C H A N G E S I N T R E N D

To explain the short-term (≈4 Myr) changes in trend along hotspottracks, if real, that are not due to changes in plate motion relativeto global hotspots, we suggest three end members for the behaviourof the lithosphere and sublithospheric source. First, if the tracksperfectly trace the zone of melting in the shallow sublithospheric

source, then over 4 Myr some melting zones may move relative toeach other. At Yellowstone, the surface and mantle tracks appear tobe parallel at least at the 8 Ma part of the track. For at least 470 kmacross the 8 Ma track of Yellowstone, the average fast direction of Swaves (244◦, Schutt et al. 1998) differs insignificantly from that cal-culated from HS3-NUVEL1A (249◦ ± 21◦ 95 per cent confidencehere and below). It also differs insignificantly from the trend pre-dicted with Yellowstone removed from the HS3 data set (252◦ ± 24◦)and from the observed trend (241◦ ± 47◦). More complex patternsof S-wave splitting have been observed from isolated measurementsin French Polynesia (Russo & Okal 1998) and Hawaii (Russo et al.1998). Second, if the magma in the lithosphere is laterally redi-rected, then short-term motion between hotspots might be createdfrom an otherwise fixed zone of melting. Flexural stresses, pre-existing lithospheric structures, existing volcanoes or lithosphericintrusions might laterally redirect hotspot magma. Hieronymus &Bercovici (1999) have shown that flexural stresses may cause pairedvolcanic loci to form from a simple source. Based on the distribu-tion of diverse seismic events beneath Kilauea volcano, its magmaconduit appears to be subvertical for the first 20 km below the

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Table 16. Consistency of HS3-NUVEL1A data when one datum or hotspot is removeda .

Removed datum or data Observed Calculated Misfitc Id �χ2e p(�χ2) f �vtg or �vr

h

length durationb ±95% ± 95%(km) (Myr) (km Myr−1)

Easter 178 5.4 −9.4 ± 65.5◦ 0.10 0.08 78% �vt − 5 ± 36Galapagos 278i 6.0i 36.5 ± 86.0◦ 0.13 0.67 41% �vt 13 ± 28Hawaiian trend 600 5.8 7.0 ± 17.2◦ 0.49 0.59 44% �vt 13 ± 31Hawaiian rate 600 5.8 16 ± 19 km Myr−1 0.74 2.94 9% �vr 16 ± 19Hawaiian segment 600 5.8 5.5 ± 17.3◦ 0.49 3.32 19% �vt 9 ± 28

15 ± 20 km Myr−1 0.74 �vr 16 ± 20Juan Fernandez 264 7.8 11.0 ± 36.6◦ 0.47 0.30 58% �vt 7 ± 24Macdonald 429 3.7 −1.9 ± 18.3◦ 0.13 0.04 84% �vt −4 ± 37Marquesas 302 2.6 19.8 ± 25.0◦ 0.07 2.38 12% �vt 40 ± 48Martin Vaz 50 1.1 14.3 ± 105.1◦ 0.04 0.07 79% �vt 12 ± 84Pitcairn 91 0.8 1.2 ± 70.6◦ 0.01 0.00 96% �vt 3 ± 145Samoa 334 2.9 −17.4 ± 23.3◦ 0.12 2.11 15% �vt − 35 ± 46Society trend 479 4.1 −2.4 ± 16.9◦ 0.18 0.08 78% �vt − 5 ± 35Society rate 479 4.1 −19 ± 21 km Myr−1 0.34 2.88 9% �vr − 19 ± 21Society segment 479 4.1 −2.4 ± 16.8◦ 0.18 2.96 23% �vt − 5 ± 37

−19 ± 21 km Myr−1 0.34 �vr − 19 ± 22Yellowstone 150 5.6 −10.8 ± 52.3◦ 0.20 0.16 68% �vt − 5 ± 24

aFor HS3-NUVEL1A, χ2hotspot = 8.0, χ2

ν = 0.80, ν = 10, p(χ2ν ) = 63 per cent.

bCalculated duration = lobs/|vcal|.cMisfit is the observed datum minus the predicted datum.d I is the data importance when estimating the HS3-NUVEL1A set of angular velocities.e�χ2 is the chi-square of HS3-NUVEL1A minus the chi-square after removing the datum or hotspot in question.f p(�χ2) is the probability of obtaining a datum as different or more different as the datum removed if the hotspots are fixed. Differences would besignificant only if p < 5 per cent.g�vt is the component of motion of the removed hotspot perpendicular to its observed trend relative to that predicted from an angular velocitydetermined after removing that trend/hotspot.h�vr is the component of motion of the removed hotspot parallel to its observed trend relative to that predicted from an angular velocity determinedafter removing that rate/hotspot.i is the observed length of Galapagos, but the duration is calculated using the rescaled length.

volcano, but becomes more subhorizontal at greater depth (Ryanet al. 1981; Klein et al. 1987). These interpretations, however, shouldbe considered tentative until confirmed both by events recordedduring the earliest years of the seismic network and by detailedsource and hypocentre characterization of recorded events. Third,

Table 17. Select statistical parameters for models with ≈4 Myr durations.

Time Span (Ma) Observed Calculated Observed Predicted Trend Calculated I �χ2 p(�χ2) �vt

length duration trend trend misfit trend ±95 per cent(km) (Myr) ±1σ ±1σ ±95% ±1σ km Myr−1

Hawaiian trend removedactive-to-3.2 409 4.0 313.5 ± 9.2◦ 289.9 ± 7.7◦ 23.6 ± 23.5◦ 300.6 ± 6.1◦ 0.44 3.6 6% 43 ± 420.0-to-4.0 492 4.8 301.9 ± 7.6◦ 293.5 ± 8.4◦ 8.4 ± 22.2◦ 298.6 ± 5.7◦ 0.56 0.5 49% 15 ± 401.0-to-5.0 419 4.1 292.7 ± 8.9◦ 311.8 ± 8.8◦ −19.1 ± 24.5◦ 301.2 ± 6.5◦ 0.53 2.1 15% −34 ± 422.0-to- 6.0 249 2.4 277.9 ± 14.8◦ 315.4 ± 10.1◦ −37.5 ± 35.2◦ 305.8 ± 8.8◦ 0.35 5.4 2% −58 ± 50

Marquesas trend removedactive-to-3.2 — — — 291.6 ± 4.4◦ — — — — — —0.0-to-4.0 116 1.0 332.1 ± 29.7◦ 289.2 ± 4.3◦ 42.9 ± 58.8◦ 290.3 ± 4.3◦ 0.02 1.9 16% 79 ± 881.0-to-5.0 302 2.6 310.0 ± 12.3◦ 287.7 ± 4.9◦ 22.3 ± 25.9◦ 291.2 ± 4.8◦ 0.15 2.7 10% 46 ± 512.0-to- 6.0 359 3.1 320.8 ± 10.4◦ 277.3 ± 8.1◦ 43.5 ± 25.9◦ 296.7 ± 6.6◦ 0.40 9.7 0.2% 77 ± 40

Same conventions as in Table 16.Active to 3.2 Ma: χ2

hotspot = 5.6, χ2ν = 0.70, ν = 8, p(χ2 = 5.6) = 70%;

0.0 to 4.0 Ma: χ2hotspot = 7.9, χ2

ν = 0.88, ν = 9, p(χ2 = 7.9) = 54%;

1.0 to 5.0 Ma: χ2hotspot = 4.2, χ2

ν = 0.61, ν = 7, p(χ2 = 4.2) = 75 %;

2.0 to 6.0 Ma: χ2hotspot = 12.3, χ2

ν = 1.8, ν = 7, p(χ2 = 12.3) = 9%.

Calculated duration is lobs/|vcal|, where vcal is calculated from HS3-NUVEL1A.Values printed in bold either (1) have differences in trend or �vt that differ significantly from zero at the ≥95 per cent confidence limit or (2) haveprobabilities of ≥5 per cent.

if the zone of melting is as broad or broader than the surface widthestimated from the dispersion of volcano locations, but the vol-canoes form above only part of the melting zone, then the trendsmeasured from the volcanoes might be irregular even if the ge-ometry of the melting zone is time invariant and magma only

C© 2002 RAS, GJI, 150, 321–361


moves vertically. At the 8 Ma section of the Yellowstone track,the basalt-covered calderas of the Snake River Plain are under-lain in the mantle by a zone of low P-wave speed that is 125 kmwide and 200 km deep (Saltzer & Humphreys 1997). This width isclose to the 130 km width we estimate for hotspot tracks on olderlithosphere. Beyond the plain, the rocks have high P-wave speed,which Saltzer & Humphreys (1997) suggest is buoyant residuum. Itremains unclear, however, how an 8-Myr-old mantle width relatesto the zone of melting beneath an active hotspot.

C O N C L U S I O N S

(1) Over the past ≈5.8 Myr, the average width of hotspot trackson older lithosphere is ≈130 km (=4σ ), as indicated by the disper-sion of volcanoes about the great circles that best fit the Hawaiian,Juan Fernandez, Marquesas, Pitcairn, Samoan and Society tracks.The width of hotspots on young lithosphere may be much wider,≈220 km, as suggested by the dispersion about the Galapagos track.

(2) These widths are many times greater than the typical 1–5 kmtransition width of magnetic anomalies due to seafloor spreading(Macdonald 1986) or the 0.5–2 km width of transform fault zones(i.e. the width of the zone of current deformation) (Fox & Gallo1984, 1986; Searle 1986). Thus current plate motion relative tohotspots can be estimated only with much lower accuracy than cancurrent relative plate motion.

(3) The uncertainties for hotspot trends and rates, which are ob-jectively estimated herein, are mutually consistent with the assump-tion that hotspots are fixed. Motion between hotspots is statisticallyinsignificant over the past ≈5.8 Myr, with the 95 per cent confidencelimit on such motion typically being ±20 to ±40 km Myr−1 and thelargest confidence limit being ±145 km Myr−1.

(4) The change, if any, in Pacific Plate motion relative to globalhotspots at 2 to 3 Ma cannot be resolved from available data. Thechange in Pacific Plate direction of motion relative to hotspots at 6to 8 Ma inferred from its change in motion relative to the AntarcticPlate also cannot be statistically significantly resolved from onlyhotspot tracks.

(5) Hotspot data sets with durations of 6–7 Myr produce stableresults, but data sets with durations of 4 Myr or less produce unstableresults.

(6) Except for the AM1 angular velocity (Minster et al. 1974) and0–3.0 Ma angular velocity of Wessel & Kroenke (1997), prior esti-mates of current motion of the Pacific Plate relative to the hotspotsdiffer insignificantly from our new Pacific Plate angular velocityrelative to the hotspots. Current Pacific Plate motion relative to thehotspots is about 50 per cent faster than its average over the past47 Ma (the age of the Hawaiian–Emperor bend; Sharp & Clague1999), but no statistically significant change in direction of motionis resolvable.

(7) Nine of the fourteen HS2-NUVEL1 angular velocities lieoutside the 95 per cent confidence region of the correspondingHS3-NUVEL1A angular velocity, while all fourteen of the HS3-NUVEL1A angular velocities lie inside the 95 per cent confidenceregion of the corresponding HS2-NUVEL1 angular velocity.

(8) There is a significant net rotation of the lithosphere relativeto the hotspots of 0.44◦ ± 0.11 deg Myr−1 (95 per cent confidencelevel) about a pole of 56◦S, 70◦E.

(9) Continental plates tend to move more slowly than oceanicplates but there is much overlap in rms velocities with, for example,the Juan de Fuca, Scotia and Nazca plates all moving slower thanthe South American, Indian and Australian plates.

(10) Plates with a substantial fraction (28–44 per cent) of theirboundary attached to subducting slabs tend to move faster than plateswith little or no slab, but with overlap in rms velocities (Forsyth &Uyeda 1975). Among the plates with substantial attached slab, thespeed tends to increase with increasing age of the lithosphere beingsubducted (Carlson et al. 1983).

A C K N O W L E D G M E N T S

AEG especially wishes to thank the many researchers who sharedtheir detailed knowledge of hotspot volcanoes. She also thanks theUS Geological Survey Postdoctoral Research program for giving herthe opportunity to spend a year at the Hawaii Volcano Observatory,thus allowing her to develop a skeptical view of Hawaii. Gary Acton,Don Argus, Dennis Geist and Bruce Buffet gave helpful reviews.Ben Horner-Johnson assisted with figure preparation. Many of thefigures were created with the plotting software of Wessel & Smith(1991). This work was supported by National Science Foundationgrants EAR-9814673 and EAR-9903763 to Rice University.

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A P P E N D I X A : D E TA I L SO F I N D I V I D UA L T R A C K S

We begin with Hawaii because the nomenclature of its eruptivesequence (preshield, shield, postshield and posterosional phases)has been applied to the other oceanic islands. After Hawaii we movesouth and the east around the globe. Details of volcano age andlocation are listed in Table 1.

Hawaii

The Hawaiian Islands are located on the Pacific Plate in the centralPacific Ocean (Fig. A1). The Hawaiian–Emperor seamount chain

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Figure A1. Bathymetric map of the Hawaiian islands. Solid triangles, Hawaiian volcanoes that have not yet ended their shield building stage; solid squares,Hawaiian volcanoes that ended their shield building as recently as 5 Ma; solid circles, Hawaiian volcanoes that likely ended their shield building before 5 Ma; ×’s,possible, but unsampled Hawaiian volcanoes. Arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertaintyover 5.8 Myr. Thin arrow shows the observed Hawaiian trend and volcanic propagation rate. Thick arrow shows motion calculated from HS3-NUVEL1A.Dashed arrow shows motion predicted by removing the Hawaii rate and trend. Geometry of on-arch volcanism from Clague et al. (1990) and Lipman et al.(1989). Geometry of flexural moat and arch (both dashed) from Menard (1964). Bathymetry is from Mammerickx (1989). Islands are shaded, even 1000 mcontours are solid, and odd 1000 m contours are dotted. Mercator projection.

consists of conical seamounts, guyots, atolls, and volcanic islands,which young to the southeast along the chain’s 6100 km length(Clague & Dalrymple 1987; Clague 1996). Four distinct eruptivestages are typical of Hawaiian volcanism, although some stagesare unknown, and possibly missing, from some volcanoes (Clague& Dalrymple 1987). Hawaiian volcanoes begin their submarinegrowth in the alkalic preshield stage (1–4 per cent of volcano vol-ume). Analyses of rocks dredged from Loihi Seamount, which is theyoungest shield volcano in the Hawaiian chain and the only exampleof preshield volcanism, suggest that preshield lavas are dominantlyalkalic basalts and basanites. The next stage is the tholeiitic shieldstage (95–98 per cent volcano volume), during which tholeiitic lavaserupt from the summit caldera and rift zones. The shield stage is fol-lowed immediately by the eruption, especially near the summit, of athin veneer of alkalic lavas. These lavas of the alkalic postshield (orcapping) stage include alkalic basalts and their differentiates out totrachytes. The low volume (1 per cent volcano volume) postshieldstage lasts less than 1 Myr, after which erosion and reef growth beginto dominate the shaping of the edifice. Up to several million yearslater, erosion is slowed briefly by the eruption of a small volume(<1 per cent volcano volume) of lavas from isolated vents. Theselavas of the alkalic posterosional (or rejuvenated) stage include alka-

lic basalts and strongly alkalic basalts such as basanites, nephelinitesand melitites. Subaerial Hawaiian volcanism typically lasts 4 Myr.We assign volcano age to be the age of the shield–postshield tran-sition (see Clague & Dalrymple (1987) for a discussion of otherassignments of volcano age). Scattered minor volumes of alkalicand strongly alkalic volcanism occur on the flexural arch aroundHawaii (Lipman et al. 1989; Clague et al. 1990). The radiogenicisotopic ratios of the north arch lavas are similar to those of someposterosional rocks and lie between those of the Hawaiian shieldstage and modern south Pacific mid-ocean-ridge basalt (MORB)(Frey et al. 2000). Along the Hawaiian Ridge, the volcanoes ap-pear to be aligned along curves (called loci) which trend up totens of degrees clockwise of the gross trend of Hawaiian Ridge(Jackson et al. 1972). As originally defined, the youngest Hawaiianislands have two loci running through them: the Kea locus (Kilauea,Mauna Kea, Kohala, Haleakala, West Maui and East Molokai volca-noes) and the Loa locus (Mauna Loa, Hualalai, Kahoolawe, Lanai,West Molokai, Koolau, Waianae and Olokele volcanoes). The geo-chemistry of these two loci may be distinct from each other in ma-jor elements and isotopic ratios (Lassiter et al. 1996; Eiler et al.1996), but the geochemistry may also vary systematically in a sin-gle locus (Ihinger 1995). Because the composition of such a small

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Figure A2. Bathymetric map of the Marquesas islands. Solid squares, volcanoes with ages of roughly 5 Ma and younger that were used to estimate trend;solid circles, volcanoes roughly older than 5 Ma; solid diamond, a likely young island; ×’s, unsampled seamounts and minor sampled seamounts. Thin arrowshows the observed Marquesas trend along its extant length roughly younger than 5 Ma. Other arrows and 2-D 95 per cent confidence ellipses are scaled toshow the displacement and corresponding uncertainty over 5.8 Myr. Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motionpredicted by removing the Marquesas trend. Bathymetry is from Mammerickx (1992a). Islands are shaded, even 1000 m contours are solid, and odd 1000 mcontours are dotted. Mercator projection.

percentage of the volcanic piles have been measured and some mea-sured samples are weathered, whether the two loci have distinctchemical styles is an open question. There are also several ways to‘connect the dots’ and not all volcanoes lie along one of the locias currently drawn (e.g. Niihau Island and Penguin Bank). Thus webase the trend of Hawaii on all volcanoes rather than on that of aparticular locus.

Marquesas

The Marquesas Islands lie on the Pacific Plate in northernmostFrench Polynesia (Fig. A2). The Marquesas archipelago consistsof seamounts and islands with a rough, SSE-younging age progres-sion along its short 350 km known length (Duncan & McDougall1974; Desonie et al. 1993). The current location of the Marquesashotspot is unknown and its track before 7 Ma may (Fleitout &Moriceau 1992) or may not exist. Although most outcrops are al-kalic, subaerial tholeiitic flows occur in the most deeply dissectedvolcanoes and in a 700-m-deep drill hole on Eiao (Duncan et al.1986; Brousse et al. 1990; Caroff et al. 1995). On Ou Pou there isa 1.6 Myr eruptive hiatus between the alkalic and tholeiitic flows(Duncan et al. 1986), while in the Eiao drill hole the change occursin <0.34 ± 0.09 Myr (Caroff et al. 1995). We assign volcano age tobe that of the oldest moderately reliable age date, which leads to veryscattered ages. When choosing volcanoes for our time windows, werely most heavily on the youngest tholeiitic ages.

Society

The Society Islands lie on the Pacific Plate in central FrenchPolynesia (Fig. A3). Diffuse volcanism is typical of the Society

hotspot throughout its history, a clear record of which exists for onlythe past 5 Myr (480 km). The volcanic island of Maiao lies 60 kmoff the main ridge of the Society Archipelago. Tetiaroa, an undatedatoll, lies 50 km off the other side of the ridge, although it mightbe part of another track. The region of active volcanism spans a di-ameter of 70 km. The tiny island of Mehetia, five large seamounts,and many more smaller seamounts are active (Cheminee et al. 1989;Hekinian et al. 1991; Binard et al. 1991, 1992a). Older low-K tholei-itic rocks have been dredged from two of the larger seamounts,Turoi and Cyana, and from some of the smaller seamounts, includ-ing Seismic Volcano 1, indicating that most of their volume formedlong ago, perhaps on ridge (Hekinian et al. 1991; Binard et al.1992a). We assign volcano age to be the age date of the youngestbasalts from the shield stage. To calculate trends we use only thoselarge seamounts from which no low-K tholeiitic rocks have beendredged.

Pitcairn

Pitcairn Island lies on the Pacific Plate in easternmost FrenchPolynesia (Fig. A4). The 1100-km-long Pitcairn–Gambier chainconsists of seamounts, atolls and volcanic islands with a well-behaved, SE-younging age progression (Guillou et al. 1993). Thelineament, although undated, continues to the NW through the Dukeof Gloucester Islands. The Mid-Pacific Mountains and some of theLine Islands may be older parts of the track (Gordon & Henderson,unpublished manuscript 1985). The neighbourhood of 0.9 Myr oldPitcairn Island (Duncan et al. 1974) is dotted with older atolls ofthe Oeno-Henderson lineament, which were possibly caused by the

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Figure A3. Bathymetric map of the Society islands. Solid triangles, volcanoes with the non-numerical age of active; solid squares, volcanoes that ended theirshield building as recently as 5 Ma; ×, unsampled Tetiaroa Atoll; asterisks, seamounts from an earlier episode of volcanism; smaller solid triangles overlyingthe asterisks, active Society volcanism occurring on the older seamounts. Arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacementand corresponding uncertainty over 5.8 Myr. Thin arrow shows the observed Society trend and volcanic propagation rate. Thick arrow shows motion calculatedfrom HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Society rate and trend. Bathymetry is from Mammerickx (1992a). Islands areshaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercator projection.

passage of an earlier hotspot (called HS2 by Okal & Cazenave 1985).The present location of the Pitcairn hotspot is marked by two largeseamounts with fresh alkalic lavas that lie about 80 km ESE of Pit-cairn (Stoffers et al. 1990; Binard et al. 1992b). Because the widthof Pitcairn is small and the plate speed high, we use this short 90-km-long segment.

Figure A4. Bathymetric map of the Pitcairn region. Solid triangle, volcano with the non-numerical age of active; solid squares, volcanoes younger than5 Ma; solid circles, volcanoes older than 5 Ma; ×’s, unsampled Henderson and Oeno atolls that may have formed by the passage of another hotspot. Thin arrowshows the observed Pitcairn trend. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertaintyover 5.8 Myr. Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Pitcairn trend. Bathymetryis from Mammerickx (1992a). Islands are shaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercator projection.

Macdonald

Macdonald Seamount lies on the Pacific Plate in southernmostFrench Polynesia (Fig. A5). The Austral–Cook chain consists ofseamounts, atolls and islands with a complex age progression alongits length of more than 2000 km (Johnson & Malahoff 1971;

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Figure A5. Bathymetric map of the Macdonald hotspot region. Solid triangle, volcano with the non-numerical age of active; solid square, a volcano roughly5 Myr old; asterisks overlain by the small solid squares, older volcanoes on which Macdonald volcanism has also occurred. Thin arrow shows the observedMacdonald trend. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertainty over 5.8 Myr.Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Macdonald trend. Bathymetry is fromMammerickx (1992a). Islands are shaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercator projection.

Dalrymple et al. 1975; Duncan & McDougall 1976; McNutt et al.1997). As early as 1964, Menard noticed the unusual intermix-ing of guyots and islands (Menard 1964). Some islands show anESE-younging progression of shield ages with a 0 Ma intercept atMacdonald, but among these are younger and older episodes ofshield- and nonshield-building (Turner & Jarrard 1982; McNuttet al. 1997). Instead of a single Macdonald hotspot, several addi-tional hotspots, including the Foundation hotspot (O’Connor et al.1998), may have passed through the Tubuai–Cook islands (Diament& Baudry 1987; Baudry et al. 1988; Gordon & Henderson, un-published manuscript, 1985; Fleitout & Moriceau 1992). Bonattiet al. (1977), Turner & Jarrard (1982), Mammerickx (1992b) andMcNutt et al. (1997) proposed or applied the concept of hot lines toocean-island volcanism that occurs in a line without the monotonicage progression required by the definition of a hotspot. To measuretrends we use only volcanoes on which no older rocks have beenfound. Thus, we discard Ra and Marotiri and keep Macdonald andRapa, although after this data set was finalized an older seamountwas found on the flank of Macdonald (Reynolds & Jordahl, pers.comm. 1999).

Samoa

The Samoa Islands lie on the Pacific Plate just north of the north-ern corner of the Tonga–Kermadec Trench (Fig. A6). The trackof the Samoa hotspot, if it exists, consists of at least 1000 kmof volcanic islands and guyots (Duncan 1985) and seamounts.Shield-building ages roughly decrease to the east (at least east from13.5 Myr-old Combe Bank), although the observed volcanic propa-gation rate is about 20 km Myr−1 slower than that predicted by platereconstructions (Duncan 1985). Another inconsistency is that shieldvolcanism has occurred in the past 0.5 Myr in the Wallis Islands(Price et al. 1991), which lie one-third of the way from 13.5 Myrold Combe Bank to the Samoa Islands. Natland (1980) suggestedthat Samoan volcanism may be caused by disturbances in the mantledue to the corner in the Tonga trench, although the He 3/He 4 ratios

in shield lavas suggest that primitive mantle is being tapped (Farleyet al. 1990; Poreda & Farley 1992). On Savai’i, Upolu and possiblyTutuila, posterosional basanites and nephelinites have erupted alonga single 110◦-striking fissure system that parallels the local strikeof the nearby Tonga trench (Natland 1980). This suggests that thestress field caused by the flexure of the subducting Pacific Plateinfluences the geometry of the posterosional volcanism (Natland1980) and by analogy may influence the geometry of the volcanolocations. While acknowledging the likely influence of the trench,we still consider Samoa to be a hotspot based on its He 3 anomaly,age progression and generally Hawaiian eruptive sequence. After fi-nalizing this data set, Rockne Volcano, which had been known onlyfrom an echo-sounding survey (Johnson 1984), was finally sampledand fresh alkalic basalts were found (Hart et al. 1999).

Galapagos

The Galapagos Islands lie on the Nazca Plate just south of theCocos Plate (Fig. A7). The Galapagos hotspot simultaneouslycreated 1000-km-long tracks on these two plates: the westward-younging Carnegie Ridge on the Nazca Plate and the SSW-youngingCocos Ridge on the Cocos Plate (Holden & Dietz 1972; Johnson &Lowrie 1972). By 5 Ma the Galapagos Spreading Centre had shiftedto the north and the bulk of the volcanism had switched from on-ridge to near-ridge (Hey 1977). Although the greatest concentrationof hotspot volcanism lies 150 to 250 km south of the spreading ridge,the Galapagos Spreading Centre still shows geochemical contami-nation by the Galapagos hotspot (Schilling et al. 1976; Verma et al.1983).

On the Nazca Plate, young volcanoes form a roughly east-west-striking island-dotted ridge (the westernmost Carnegie Ridge) anda NW-striking chain of isolated volcanoes (the Wolf–Darwin lin-eament). The basalts from the archipelago have variable incompat-ible elements and isotopic ratios, which range from those similarto the contaminated MORB’s of the Galapagos spreading centreto those typical of ocean-island basalt (OIB) (Geist et al. 1988;

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Figure A6. Bathymetric map of the Samoa islands. Solid squares, volcanoes younger than 5 Ma; solid diamonds, young, but undated volcanoes that wereused to calculate the trend; ×’s, unsampled Rose Atoll and Rockne Volcano, which was confirmed to be active after this data set was finalized. Thick,solid line is the active plate boundary (Brocher & Holmes 1985). Thick, dashed line is the posterosional fissure system of Natland (1980). Thin arrowshows the observed Samoa trend (although some radiometric dates from the Wallis Islands indicate they are younger than 5 Ma, there were not used toestimate trend). Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertainty over 5.8 Myr.Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Samoa trend. Bathymetry is fromMammerickx (1992a). Islands are shaded, even 1000-m contours are solid, and odd 1000-m contours are dotted. Mercator projection.

Figure A7. Bathymetric map of the Galapagos islands. Solid triangles, volcanoes with the non-numerical age of active; solid squares, volcanoes younger than5 Ma; solid circle, a seamount older than 5 Ma. Angular curve is the approximate active plate boundary. Thin arrows show the observed Galapagos trends alongthe Carnegie Ridge and Wolf–Darwin lineament. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and correspondinguncertainty over 5.8 Myr. Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Galapagostrend. Bathymetry is from Mammerickx & Smith (1980). Islands are shaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercatorprojection.

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Figure A8. Bathymetric map of the Easter Island region. Solid triangles, volcanoes in the Volcanic Field Group (these have the non-numerical age of active);solid squares, volcanoes with ages of 5 Ma and younger. Thin arrow shows the observed Easter trend (Sala y Gomez was not used to estimate trend). Otherarrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertainty over 5.8 Myr. Thick arrow shows motioncalculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Easter trend. Island outline is from Hagen et al. (1990) and bathymetryis from GEBCO (1982). Islands are shaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercator projection.

Harpp & White 1990; McBirney 1990; White et al. 1993). In gen-eral the MORB-like basalts occur along the centre of the CarnegieRidge while those typical of OIB’s occur along the periphery of theridge and along the Wolf–Darwin lineament (Harpp & White 1990;McBirney 1990; Geist 1992; White et al. 1993). Based on limitedvertical exposures (due to low erosion rates, Standish et al. 1998),each island seems to have a different eruptive history (Geist 1992),which may include shield building, fissure eruption, caldera collapseand normal faulting (e.g. Geist et al. 1985, 1986; Vicenzi et al. 1990).The Wolf–Darwin lineament may form by the sublithospheric chan-neling of the hotspot source to the spreading ridge (Morgan 1978).Because the Wolf–Darwin volcanoes are isostatically compensatedand have ages younger than the seafloor, Feighner & Richards (1994)instead suggest these islands overlie a fault. Volcanism has occurredon most of the islands in the Galapagos archipelago in the past0.1 Myr (White et al. 1993). Based on rocks dredged from theCarnegie Ridge, a broad distribution of volcanism (at least 140 kmmeasured west to east) has been typical of the Galapagos hotspotfor at least the past 6 Myr (Sinton et al. 1996). Because there is noknown consistent eruptive sequence, we assign volcano age to bethe oldest age estimate that we judge to be moderately reliable. Al-though some small young seamounts have been dredged and datedalong the Carnegie Ridge (e.g. Sinton et al. 1996), to have a uniformdata set we only use subaerial volcanoes, except for one submarinefeature that is 5.8 Myr old.

Easter-Sala y Gomez

The islands of Easter and Sala y Gomez lie on the Nazca Plate justeast of the Easter microplate (Fig. A8). The young volcanism thatoccurs on these islands as well as that at San Felix and Pitcairn ledBonatti et al. (1977) to propose that the extensive volcanism wascaused by a hot line. Treated as a single hotspot, the track of

the Easter-Sala y Gomez hotspot consists of the older mirror-image northern Tuamotus on the Pacific Plate and the NazcaRidge on the Nazca Plate and the younger, non-mirrored Sala yGomez Ridge on the Nazca Plate (Pilger & Handschumacher 1981;Okal & Cazenave 1985). Limited age dates along the Sala yGomez Ridge show monotonic westward younging (O’Connor et al.1995). On the Pacific Plate the en echelon ridges between CroughSeamount and the Easter Microplate might be a weak youngPacific hotspot track (Hekinian et al. 1995) or they might be re-lated to the Easter Microplate (Binard et al. 1996). The spread-ing centres of east and west rifts of the Easter Microplate eruptE-MORB, which contains slightly more incompatible elements thannormal MORB, with highly radiogenic lead (Hannan & Schilling1989; Haase et al. 1996). Eastward of the microplate, the Nazcanseafloor is barren of recent volcanism for 130 km until the ac-tive Ahu and Umu volcanic fields are reached (Hagen et al. 1990;Stoffers et al. 1994). In the 100 km span between these volcanicfields and Easter Island lie two seamounts having older lavas thatare similar to those of the tholeiitic volcanic fields, but havingyounger lavas that are transitional and similar to many of the olderrocks on Easter Island (Haase et al. 1997). Using the volcano andridge geometry and major, trace and unstable elements, Haase et al.(1997) divided Easter volcanism into three, possibly time sequen-tial groups: first, the tholeiitic Volcanic Field Group; second, thetransitional Main Group; and third, the transitional, but more differ-entiated Roiho Group. Based on modelling of major, trace, and un-stable elements, the deepest and hence hottest mantle temperaturesoccur beneath the volcanic fields (Haase et al. 1996), indicating thatthe tholeiitic volcanic fields, rather than the islands, best mark theactive hotspot. Using an overlapping set of geochemical data, Pan& Batiza (1998) suggest instead that the sublithospheric hotspotsource is under Sala y Gomez Island. Neglecting the conflictingpetrologic modelling, we prefer the first interpretation because geo-morphologically Sala y Gomez volcano is older than Easter Island.

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Figure A9. Bathymetric map of the Juan Fernandez region. Solid squares, volcanoes that are likely younger than 5 Ma. Thin arrow shows the observed JuanFernandez trend. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertainty over 5.8 Myr. Thickarrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Juan Fernandez trend. Bathymetry is fromGEBCO (1982). Islands are shaded, even 1000 m contours are solid, and odd 1000 m contours are dotted. Mercator projection.

We assign volcano age to be the age of the transition between theVolcanic Fields Group and Main Group. We use only the volcanoesof Easter Island and westward to estimate the observed trend.

Juan Fernandez

The Juan Fernandez Islands lie on the Nazca Plate in the southernPacific Ocean (Fig. A9). The track consists of two westward-younging main islands and many isolated seamounts that span800 km and disappear into the Peru–Chile trench (Stuessy et al.1984). Because the stratigraphy of the islands is poorly known anddated, we assign volcano age to be the oldest radiometric date oneach island.

Yellowstone

The Yellowstone hotspot lies on the North American Plate and itstrack spans at least 800 km and 16 Myr (Fig. A10) (Morgan 1972;Armstrong et al. 1975; Suppe et al. 1975; Pierce & Morgan 1992;Smith & Braile 1994). The track is marked by bimodal volcan-ism (rhyolites and basalts) at its young, northeast end and thickflood basalts underlain by older bimodal volcanics along the restof its length (Armstrong et al. 1975; Leeman 1982). For the past2.2 Myr, bimodal eruptive activity has been restricted to the Yellow-stone Plateau volcanic field (Armstrong et al. 1975; Christiansen1982). The Yellowstone field consists of three overlapping and par-tially nested calderas, which formed by the eruption of huge rhyoliticash-flow sheets, and a much smaller volume of basaltic and rhy-olitic flows (Christiansen & Blank 1972). Volcano location of thesecalderas is the centre of moment of the caldera. Rhyolitic magmafor the next catastrophic eruption may be accumulating in the upper

crust beneath the northeastern rim of Yellowstone caldera. Evidencefor this magma body includes low P-wave speed and low gravity,both of which are consistent with a 10–50 per cent partially meltedrhyolitic body (Lehman et al. 1982; Schilly et al. 1982). Because aparabolic zone of normal faulting progresses with the rhyolitic ashflow volcanism (Anders et al. 1989), the geometry of the Yellow-stone track may poorly reflect the velocity of the North Americanplate relative to a global hotspot model (Rodgers et al. 1990). InHS3-NUVEL1A, however, the misfits of Yellowstone are quite typ-ical, suggesting that whatever complexity is added by the Basinand Range, it is not significantly greater that what is happening atoceanic hotspots. For example, the observed and predicted Yellow-stone trends differ only by 11◦ ± 52◦ (95 per cent confidence hereand below) (Table 16). The observed and predicted Yellowstone ratesdiffer only by 9 ± 32 km Myr−1, which is less than the 16 ± 19 kmMyr−1 misfit of Hawaii and the 19 ± 21 km Myr−1 of Society(Table 16).

Martin Vaz

The island of Trindade and the nearby islands of Martin Vaz lie onthe South American Plate in the south Atlantic Ocean about 1400 kmeast of Rio de Janeiro (Fig. A11). The eastward-younging track ofthe Martin Vaz hotspot consists of volcanic islands, guyots, conicalseamounts and alkalic rocks of the Sao Paulo–Rio de Janeiro littoralbelt (Almeida 1961; Burke & Dewey 1973; Baker 1973; Herz 1977).We assign the age of Trindade to be 3.35 ± 0.29 Myr, which is theoldest K–Ar date from one of the less altered samples from the basalcomplex (Cordani 1968, 1970). The easternmost island group, IlhasMartin Vaz, has one K–Ar date of 60 Ma, which is inconsistent with

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Figure A10. Map of the Yellowstone hotspot region. Solid triangle, the centre of the zone of low wave speed; solid squares, the centres of calderasthat erupted huge rhyolitic ash-flow sheets since 5 Ma; solid circles, the centres of calderas that erupted huge rhyolitic ash-flow sheets before 5 Ma.The approximate boundaries of all six calderas are outlined in various patterns (Christiansen 1984; Pierce & Morgan 1992). Thin arrow shows the ob-served Yellowstone trend. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and corresponding uncertainty over5.8 Myr. Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the Yellowstone trend. Mercatorprojection.

Figure A11. Bathymetric map of the Martin Vaz islands. Solid square, volcanoes that are likely younger than 5 Ma; ×, unsampled nearby seamount. Thinarrow shows the observed Martin Vaz trend. Other arrows and 2-D 95 per cent confidence ellipses are scaled to show the displacement and correspondinguncertainty over 5.8 Myr. Thick arrow shows motion calculated from HS3-NUVEL1A. Dashed arrow shows motion predicted by removing the MartinVaz trend. Bathymetry is from Cherkis et al. (1989). Islands are shaded, even 1000-m contours are solid, and odd 1000-m contours are dotted. Mercatorprojection.

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the young age of Trindade, and another date of <0.73 Ma, whichsuggests there may have been a mix up in the samples (Cordani1970). Because the width of Martin Vaz is small and the plate speedmoderate, we use the trend from this short (50-km-long) segment.

A P P E N D I X B : L E N G T H O F T I M EI T TA K E S A V O L C A N O T O G RO W

Straight-line fits to assigned volcano age vs distance along theHawaii and Society chains both indicate that it takes 0.7 Myr to buildvolcanoes in these chains (Table 2). The estimate of 0.7 Myr neglectsthe time elapsed while 1-km-deep Loihi and 3-km-deep Volcano 16grew to their current sizes. Hawaiian volcanoes are roughly spaced

35 km apart when projected onto a single trend. If we assume thenext Hawaiian volcano is about to erupt 35 km from Loihi andextrapolate from the observed Hawaiian volcanic propagation rate,then this hypothetical volcano would end its shield building 1.1 Myrfrom now. Prior estimates of the time it takes to grow a Hawaiianvolcano through shield building are 0.5–1.5 Myr (Jackson et al.1972), 0.2 Myr (Wright et al. 1979), and 0.6 Myr (Moore & Clague1992). As the duration of the main phase of volcano growth we use0.8 Myr, which follows from a fit to the Hawaiian rate from vol-canoes from Waianae (3.1 Ma) and eastward, which lies betweenour two estimates (0.7 Myr and 1.1 Myr) above, and is close tothe most recent independent estimate (i.e. that of Moore & Clague1992).

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